There's no canon evidence as to what happened to the Denobulans after Star Trek: Enterprise, but we can make a reasonable guess.
According to Captain Picard's dialog in Star Trek: First Contact, the Federation consists of over one hundred fifty member worlds. If we assume that means there are roughly one hundred fifty species in the Federation, it's not surprising that there are no mention of Denobulans in any of the later series.
The Memory Alpha page for Federation members lists only about thirty-five Federation species seen on screen, which means there are at least one hundred fifteen Federation species we've never seen on screen either.
In fact, there's no canon evidence that the Denobulans ever even joined the Federation. They may have simply maintained a diplomatic relations with the Federation (or not) over the next few centuries, instead of becoming Federation members, making their lack of appearance in any of the other series even less surprising.