Can a software bug appear even after the software has been running fine for a while?

There was this question about the awards bug in fluther, and it made me wonder whether a bug can appear after a while, or if it could only occur when an update is installed? If it can occur after a while, how come?

What is the best strategy to deal with the bug? Would it be advisable to go back to a previous version of the software that worked, leave it alone (if the feature wasn’t important) or fix it?