The volunteer-run festival is held in Keynsham Memorial Park, and as well as music, includes art and dance workshops, entertainers and comedy acts.
Mr May said it would be more than just entertainment that would be lost if the festival were to close.
In recent years, the organisers have hosted a two-hour mini-festival for people with dementia after realising the main festival could be too overwhelming.
Mr May said this event provided a “very safe and welcoming environment”.
He added: “It’s a very emotional event, because you can see people living with dementia come alive.
“[They] remember this song, they start dancing and they start enjoying it all.”