Is it correct that a person who sneezes says Al-Hamdu Lillaah at the first three times he sneezes only?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

An-Nawawi stated that there is a consensus among the scholars that it is desirable for a person who sneezes to say: "Al-Hamdu Lillaah" (All perfect praise be to Allaah). The evidence is that Abu Hurayrah reported that the Prophet said: "When a person sneezes he should say: Al-Hamdu Lillaah." [Al-Bukhari] This narration is reported in a general context and we have not come across any Prophetic narration which restricts this to three times. It appears from your question that what you meant is what the scholars stated that it is permissible not to say "Yarhamuka Allaah" (May Allaah have mercy on you) to the person who sneezes more than three times. That is because if a person sneezes more than three times consecutively, it is most likely that he has a cold. The evidence is that Salamah Ibn Al-Akwa' narrated that a man sneezed in the presence of the Prophet . The Prophet told him: "Yarhamuka Allaah" (May Allaah have mercy on you). When he sneezed the second and third time, the Prophet said (after the third time): "This man has a cold." [At-Tirmithi] In another narration he said: "One should say to a sneezing person ''Yarhamuka Allaah" (May Allaah have mercy on you) for the first three times he sneezes, if he sneezes more than three times, then he has a cold."

Allaah Knows best.