I can't see any reason to dispute the grammaticality of fall back asleep, but two things that did (mildly) surprise me when I looked into usage patterns were:-
- It's almost as common as fall back to sleep (which version sounds far more natural to me).
- Both usages were relatively uncommon until just a few decades ago.
(I see no evidence of any significant US/UK split in terms of either preference or prevalence.)
My guess is that both OP and I find the asleep version less acceptable because it doesn't fit the same pattern as go back to sleep (where go back asleep is virtually unknown).
