Your question is asked by the Ben Yehodaya, written by the author of Ben Ish Chai - Rabbi Yosef Chaim, zt'l, of Baghdad and he gives an answer based on the Kabalistic interpretations.

The Ben Yehodaya cites the Zohar and the Arizal, that in fact Esther herself did not have relations with Achashverosh, but instead there was a "Shidah" - a demon - who appeared instead of Esther whenever Achashverosh wanted to have relations with her.

The Ben Yehodaya writes that in fact Esther went miraculously from Achashverosh's palace to Mordechai's house so that nobody could see her (see also Tosfos below 15a DH k'Shem who writes that the reason Mordechai did not want to divorce Esther was because since one needs two witnesses in order to give a Get, Mordechai was afraid that this way the matter may become known to the king. One learns from Tosfos that Mordechai was trying to keep the whole thing quiet). One is forced to say that this miraculous journey was accomplished by uttering the explicit Name of Hash-m.

[There is a source in Shas for this possibility of travelling distances by reciting Hash-m's Name. See Gitin 89a where the Gemara states that we are not worried about Mamzerus. The Rosh (Kidushin 4:7) writes in the name of the Ba'al Halachos that this refers to a scenario where the husband went overseas and his wife had a baby. We are not concerned that the wife may have been unfaithful because we say instead that the husband may have come home quietly and had relations with her. There is a precedence for this in the Talmud Yerushalmi which states that Shmuel's father came home through uttering Hash-m's Name, and had relations with his wife.]

When Esther saw that Achashverosh wanted to have relations her, she recited Hash-m's name in order to bring the "Shidah" in her place. With the same Name of Hash-m she also achieved another miracle simultaneously by enabling herself to disappear from everyone's sight. She could see others, but nobody could see her. This way she managed to escape to Mordechai's house.

KOL TUV

Dovid Bloom

(1) It seems that they did not consider the risk of sending messages through the intermediary quite as dangerous as Esther actually going to Mordechai's house. In fact it is not clear that danger did come out of these messages in the end. See Tosfos Bava Basra 4a DH she'Kol who cites the Targum that learns from Esther 4:12 "And they told to Mordechai the words of Esther", that it was other people who had to convey the message because Hasach (i.e. Daniel) had been killed by Haman for his intermediary services. However Tosfos writes that our Gemara maintains that Hasach was not killed, because our Gemara in Megilah 15a gives a different reason why other people had to pass on the messages.

(2) One should not forget that it was public knowledge that Esther was brought up in Mordechai's house. The secret was that Esther was Jewish. Ben Yehoyada also explains that people thought that Mordechai had found an "Asufis" i.e. had found an abandoned baby in the street and brought the baby up. Nobody actually knew for sure which race she belonged to, but the Gemara (above 13a) says that Esther appeared to everyone in the country as if she belonged to each person's nation. This is why she was so popular. Ben Yehoyada also explains with this what the Gemara (above 13a) states that Esther gave Achashverosh Jewish food to eat. This did not arouse suspicions that she was Jewish because people merely assumed that the reason she was familiar with Jewish cuisine was because she had grown up in Mordechai's household.

(3) In the light of the above it is not so surprising why Esther and her supposedly adopted father, Mordechai, should be sending messages back and forth. However Yalkut Me'am Lo'ez explains that the reason that some commentaries maintain that Haman killed Hasach was because he got suspicious from the frequency of the communications that there was some plot brewing between Esther and Mordechai. Even though Haman did not know that Esther was Jewish, he still suspected she would be pro-Jewish because of her connection with Mordechai and therefore would try and foil Haman's plot.

(4) Indeed, according to the versions that Hasach was killed, the Yalkut Shimoni (4:12) relates that ha'Kadosh Baruch Hu said that since Haman killed Hasach, Esther could from now on use the Holy spirit (Ru'ach ha'Kodesh) to communicate with Mordechai. The Targum states that from then on, the angels Micha'el and Gavri'el appeared and conveyed Esther's messages to Mordechai.

(5) Another thing to remember is that we always try to avoid using miraculous means wherever possible. See Gemara Ta'anis 24b where Rava was criticized for "troubling Hash-m" too much by exaggerating in his requests for rain. Nearer our times, it is told of the Chafetz Chaim (see Or Yechezkel 6:133, by R. Yechezkel Levinstein zt'l) that during World War 1, many fled from Poland to Russia. The Chafetz Chaim was also seriously considering leaving his small town of Radin but was uncertain what to do. It was suggested to him that he should use the Goral ha'Gra - the "lottery" ascribed to the Vilna Ga'on - to find the appropriate verse in the Torah which would tell them what to do. The Chafetz Chaim refused and explained that he did not want to put Hash-m to trouble by employing a special way of conducting the world, which would make him obligated to Hash-m from now on in a way that he may never be capable of paying back.

(6) Now we can understand a little that it was justified for Esther to use supernatural methods to save herself committing the grave transgression of relations with Achashverosh, whereas to avoid the small danger of getting caught sending messages to Mordechai it was not worth employing special forces.

KOL TUV

Dovid Bloom

Your question is asked by Ben Yehodaya, written by the author of Ben Ish Chai - Rabbi Yosef Chaim, zt'l, of Baghdad and he gives an answer based on the Kabalistic interpretations.

Ben Yehoyada cites the Zohar and the Arizal, that in fact Esther herself did not have relations with Achashverus, but instead there was a "Shida" - a demon - who appeared instead of Esther whenever Achashverus wanted to have relations with her.

BY writes that in fact Esther went miraculously from Achashverus' palace to Mordecai's house so that nobody could see her (see also Tosfos below 15a DH k'Shem who writes that the reason Mordecai did not want to divorce Esther was because since one needs 2 witnesses in order to give a Get, Mordecai was afraid that this way the matter may become known to the king. One learns from Tosfos that Mordecai was trying to keep the whole thing quiet). One is forced to say that this miraculous journey was accomplished by uttering the explicit Name of Hash-m.

[There is a source in Shas for this possibility of travelling distances by reciting Hash-m's Name. See Gitin 89a where the Gemara states that we are not worried about mamzerus. The Rosh (Kidushin 4:7) writes in the name of Baal Halachos that this refers to a scenario where the husband went overseas and his wife had a baby. We are not concerned that the wife may have been unfaithful because we say instead that the husband may have come home quietly and had relations with her. There is a precedence for this in the Talmud Yerushalmi which states that Shmuel's father came home through uttering Hash-m's Name, and had relations with his wife.]

When Esther saw that Achashverus wanted to have relations her, she recited Hash-m's name in order to bring the "Shidah" in her place. With the same Name of Hash-m she also achieved another miracle simultaneously by enabling herself to disappear from everyone's sight. She could see others, but nobody could see her. This way she managed to escape to Mordecai's house.

KOL TUV

Dovid Bloom

Follow-up reply:

Here is a different and simpler answer to your question. Achashverus did not object to Esther going frequently to Mordecai's house because he knew that Mordecai had brought her up as a young girl. However what Achashverus did not know was that Mordecai had married Esther. This they managed to keep secret, and therefore Achashverus did not realize that Mordecai and Esther were living together as husband and wife (maybe this was the miracle that they succeeded in keeping this secret from everyone).

Chag Kasher v'Samaech

Dovid Bloom

The Ben Yehoyada cites as the source for his explanation the Zohar and the Arizal so it seems in fact that there is a dispute between the Zohar and our Gemara about whether there were actually physical relations. This means that there is a dispute in Chazal about this point because the Zohar was written by Rabbi Shimon bar Yochai, who was a Tana. (I once saw that the Rema in the Darkei Moshe wrote this Sevara - I cannot find the reference at the moment). For cases where there is a dispute between the Gemara and the Zohar see Mishneh Berurah 25:42 that the Halachah follows the Gemara.

As I mentioned in a follow-up answer to this question, the simple way of understanding how Achashverosh allowed Esther to have relations with Mordechai (i.e. not according to the Zohar) is because he knew that she had grown up in his house so was not against letting her visit him. However Achashverosh did not know that Mordecai and Esther were husband and wife and she managed to keep this secret from him. In addition Achashverosh did not think that Esther was Jewish but thought she was an abandoned baby from a different nation that Mordechai had taken into his house.

KOL TUV

Dovid Bloom