I know from experience (and this link) that sleeping monsters regain a portion of their missing health, so long as they aren't interrupted during their nap.
Exactly how much health do sleeping monsters regain? Is it all of their health or only a small portion? I only know that it's enough to keep them from being captured if they were limping beforehand.
Best Answer
That's exactly it - they regain enough to get out of the limping/capturable threshold. This generally corresponds to around 25% of their maximum HP for the later monsters (anything past a Royal Ludroth) and 40% or so for Ludroths and bird wyverns. Note that attacks on a sleeping monster gain bonus damage, so hitting them while sleeping will push them back below the capturable threshold.