Hash ratchets with truncating hash function
Collisions in the hash will make fewer and fewer keys possible based on the number of iterations, resulting in a sort of "entropy loss". (Aside, I don't think "entropy loss" is the correct term as the system is deterministic and the entropy is provided by the original key.)

Importantly, though, the effect will be very small with a 256 bit hash, as covered by this question.

In short, "yes, but not enough to matter from a security perspective".

I would add a 64-bit counter variable to that hash step as is done in some KDF and password-hashing constructions to ensure there is no chance of falling into a short cycle of keys - no matter how unlikely such a cycle would be.