It's becoming more and more common to take some time off before doing fellowship, most especially for the competitive specialties (of which endo is not one of them). And there are usually lots of endo spots open every year, so if you aren't particularly picky about where you go, you can sometimes get a spot after the match to start the next July.
I don't know if there is a specific limit, though I don't think many people avoid fellowship for more than 3-4 years. And you have to pass your peds boards before you can be eligible for subspecialty boards (though I'm not sure if peds neurology qualifies, since that's a weird fellowship path that isn't through ABP).