When police obtain an arrest warrant, they're supposed to try to arrest the suspect as soon as possible, but there's little the suspect can do if this doesn't happen. In general, arrest warrants remain open until the suspect is apprehended. They usually do not expire, but there are some exceptions.
Suspect Can Challenge Arrest Delay in Court
The only way to challenge a lengthy delay between the issuance of a warrant and your arrest is to try to get a court to dismiss the warrant. You can try to argue that the delay violated your constitutional right to a speedy trial. But the delay must usually amount to several years, and it cannot have been caused by your attempt to avoid arrest.
Expiration of Warrants May Vary by State
Some states have laws that regulate the expiration of warrants. Indiana law requires that arrest warrants for misdemeanors expire after 180 days or six months, although a felony warrant is never allowed to expire. Even when a misdemeanor warrant expires, the prosecuting attorney can request that the court issue a new one.
There's no blanket rule that covers all 50 states, so if you think there may be an outstanding arrest warrant out for you, contact legal aid or an attorney in your area for assistance.