How often can dental abscesses fully heal on their own?

NEVER (RARE): While it is not impossible, it would be rare at best and most likely never. Dental abscesses need to be professionally treated.

They don't: Since an abscess is the result of an infection, they really dont resolve without treatment.

Depends on cause: Dental abcesses generally do not heal on their own and tend to get worse. You need to see a dentist to determine the cause.