I'm not quite sure, but I think a president can be elected only twice in Poland (the same person). But even if he could become a president for the third time, I think people were tired of him, and wanted a change (they didn't really appreciate him then; they do now instead :) Typical).
So they voted for Aleksander Kwasniewski, who looked good (much better than Walesa, and looks ARE important), and had a catchy tune for his campaign.
Walesa also got a peace Nobel price, in 1983.
Sylwia