> are there encryption methods that actually do not suffer from reductions in randomness or entropy etc when just simply running the algorithm on the encrypted output multiple times?

Unless you can prove that all e.g. 2^256 possible 256 bit inputs map to 2^256 different 256 bit outputs (for every key, in the case of encryption), then chances are you lose strength with every application because multiple inputs map to the same output (and consequently some outputs are not reachable).