If the heroes claim victory but there are still search tokens remaining, can the heroes take actions to search?

This is particularly important for 'chase' scenarios like the Masquerade Ball, where the characters might not have time to take an action to search before the villain escapes.

It seems counter-intuitive that by winning you lose the opportunity to claim treasure, but I can't find anywhere in the books that state what happens.

We play that once the encounter has been won, no one else may take an action. To me, this makes sense because there are instances where it would be more beneficial to end a quest to win the main objective rather than continue on and try and get the search tokens. It adds additional strategy in my opinion.

No. After an Encounter/Quest is won, no further actions can be taken. Any uninvestigaed Search tokens are lost. May seems counter-intuitive, but allowing heroes to collect Search Tokens afterward is horribly unbalanced.