He had contacts with Christian leaders of the period, debating religious and philosophical topics with them. His position was challenged on a number of occasions following allegations that he was a secret follower of the Shabbateanism, an outlawed movement centered around the false messiah Shabtai Zvi, despite Rabbi Eybeshitz supporting the excommunication of all Shabbatean followers.
The controversy over whether Rabbi Eybeshitz was a Shabbatean spread to all major Jewish communities, and attacks by opponents lasted until his death.
Thirty of his works in the area of halakhah (Jewish law) have been published. In addition, several of his works on homiletics, teaching methodology, and Kabbala are currently in print.
It is interesting to note that only one of his works was published in his lifetime. The posthumous printing of so many of his works is testimony to his influence on his contemporaries through his oral teachings and his personality.
Sources: Orthodox Union