Possibility of the encrypted text being the same as the supplied plain text!
For a fixed key, a block cipher is presumed to behave like a pseudo-random permutation (PRP) over messages.  What we are interested in is if the permutation contains a fixed point, i.e. if it is a derangement or not.  What we find is that there is about a 63% chance that there is at least one fixed point, and the expected number follows a Poisson distribution (i.e. there shouldn't be many).

Your argument about short messages doesn't apply to block ciphers used in practice, since they don't operate on messages smaller than a block.