Is it possible to get dry socket twice on the same wisdom tooth?

Yes, but unlikely.: If the clot has been disturbed , a dry socket post-extraction can occur...Especially in smokers. Usually a medicated dressing is changed every other day or so which would prevent the formation of another dry socket, or exposed bone.

Very unlikely: Once treated the first time, then it is very unlikely. If there are still issues from the removal of the wisdom tooth, then see an oral surgeon.