Yes, there should be a period after the closing parenthesis.
The general principle is that a sentence should remain structurally valid if the parenthetical brackets, and everything enclosed by them, are removed.
The text within parentheses can be a whole sentence (several sentences?), but I don't think it's acceptable for the "enclosing" sentence to continue after the closing bracket, if one or more periods (exclamation/question marks don't count!) appear in the parenthetical text.
Thus, for example, this statement ends with a period after the final word "here". (Following the principle outlined above, I can parenthesis multiple sentences, but in this case they aren't "part of" any enclosing sentence. Thus the second parenthesised sentence ends with a period before the closing bracket, after this word "here".) Even if there's no actual "rule" saying I can't, it would be clumsy if I'd replaced the word (and corresponding symbol!) "period" in that statement with "comma", and started this supplementary statement with "but even"!