Expire as in like a paid licensed product? No.
However, it will become incompatible with newer versions of packaged workbooks. That is to be expected from software. Since Tableau Reader is free this shouldn't be an issue, simply download the latest version: Tableau Reader | Tableau Software
Its free and does not expire.Only keep updating
Thanks both for your updates..
Overall conclusion/understanding that, Reader does not expire, however need to upgrade the versions frequently.