Should the words of tashmit (asking God to bestow his mercy on a person who sneezes) be said to a person once or after every time he sneezes?

Lexically, tashmit is supplicating God seeking His kindness and blessings. In Islamic law, it is supplicating God for one who has sneezed by seeking His mercy for him. It is a sunnah for a person who sneezes to praise God the Almighty after which a fellow Muslim is to pronounce the words of tashmit which is “Yarhamukum Allah.” The one who sneezed can reply by saying, "Yahdikum Allah wa yusliha balakum (may God grant you guidance and peace of mind)". This is based on the hadith recorded by Bukhari in his Sahih through Abu Huraira (may God be pleased with him) who narrated that the Prophet (God’s peace and blessings upon him) said, "When any of you sneezes, he is to say, 'Al-hamdu-lil-Lah' (praise be to God) and his fellow brother or companion is to tell him, "Yarhamuk Allah (may God have mercy on you). Then the person who has sneezed should reply and say, 'Yahdeekum Allah wa yusliha balakum."

If someone sneezes more than twice or thrice, this might mean they are suffering from a cold and in which case, we must follow the Prophetic guidance and supplicate God for them with a suitable supplication by asking God for their recovery. A person must not pronounce tashmit to another who sneezes more than twice or thrice. The legal premise for this is the report recorded by Muslim and al-Tirmidhi through Salama ibn al-Akwa' (may God be pleased with him) who said, "The Prophet said the words of tashmit to a man who sneezed twice by saying, 'May God bestow his mercy on you.' When the man sneezed a third time, the Prophet said, 'This man has a cold'" (The report is in the words of al-Tirmidhi).
God the Almighty knows best.