Nixon was not-quite impeached, but the offenses for which he *almost* was tried -- he avoided trial only by resigning -- occurred near the end of his first term, as part of his effort to be re-elected, and came to life only after said re-election, early in his second term.

So: Yes, Amos, the "high crimes and misdemeanors" for which a President can be impeached need not have occurred since his most recent re-election. They *may* need to have occurred during his current (multi-term) tenure, but it doesn't matter if he's already in the second term and the bad stuff happened during the first.