What is the ruling on the fast of one from whose teeth blood always emerges, which is difficult to guard against? Is he sinful for not treating his teeth? And is he required to make up the fast after treatment?

If blood continuously exits the mouth and is difficult to guard against, then it is excused, and swallowing it does not invalidate the fast, according to the opinion of some scholars, and this offers ease. Therefore, your fast is valid, and you are not required to make up Ramadan. It is stated in "Fath al-Ali al-Malik" that if such blood becomes frequent and continuous for someone, it is excused for him, so he is not commanded to expel it or wash it, and his fast is not broken by swallowing it. As for refraining from medical treatment, there is no sin in it.