I haven't had the Report button disappear like that, and I've used it quite a few times, though I don't think I ever saw 20 in one session. If it were a timed limit (only X number can be sent in a given period of time), I'd expect an error message to appear rather than the report button itself to disappear.

I have seen a marked decrease in the amount of spam since this feature went live.

It would be nice, though, if it automatically added the characters you report to your blacklist rather than making reporting and blacklisting them two separate actions. (Of course, blacklisting would have to remain a separate option for cases where you want to BL people for reasons other than spam, but I can't imagine the other way around, of reporting someone and not also wanting them blacklisted.)