Is there something incorrect about the phrase "fall back asleep"?
A quick Google search shows that the phrase seems to be in relatively common usage, but for some reason I find the construct very awkward.
I would say "fall asleep" the first time, and then "fall back to sleep" if awakened.
Saying "fall back asleep" sounds wrong to me in a similar way to "(I tripped but am) back running". Is something wrong with the tense? A case of "coming back to the present"?
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 myself 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).