When does a Missouri bench warrant expire?

NEVER, as is the case for any warrant.

NEVER is not the case for all bench warrants and its certainly not the case for all arrest warrants.....

A Bench warrant will stay active till you are either brought before the court,the court drops the warrant itself, you die or you do some legal action to resolve the warrant.

In some city courts, bench warrants for traffic tickets and unpaid fines are sometimes cleared after a number of years but that is a city by city issue.

There are statute of limitations set on arrest warrants(meaning you committed a crime but have not been arrested by the police) that vary from state to state and once the statute of limitations is reached for that specific crime you can not be prosecuted for that crime and the arrest warrant becomes void,such as an arrest warrant issed in the state of Maryland in 1956 for a person who committed petty theft would no longer be valid in 2012 because the states statute of limitaions on the crime of petty theft is only 20 years..