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:-

1. It's almost as common as *fall back **to** sleep* (which version sounds far more natural to me).  
2. Both usages were [relatively uncommon][1] until just a few decades ago.

![enter image description here][2]

(I see no evidence of any significant US/UK split in terms of either preference or prevalence.)

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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][3]).


  [1]: https://books.google.com/ngrams/graph?content=fell%20back%20asleep,fell%20back%20to%20sleep&year_start=1900&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1;,fell%20back%20asleep;,c0;.t1;,fell%20back%20to%20sleep;,c0
  [2]: https://i.sstatic.net/YiiUi.png
  [3]: https://books.google.com/ngrams/graph?content=go%20back%20asleep,go%20back%20to%20sleep&year_start=1900&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1;,go%20back%20asleep;,c0;.t1;,go%20back%20to%20sleep;,c0