Will a warrant in washington state ever go away

You need to go back to the court that issued that warrant and have it vacated. Its not just going to go away because you want it to. You are now also possibly facing violation of probation charges as well. You may want to talk to a lawyer but you should voluntarily surrender (it's better than the alternative).

Bench warrants for failure to appear or complete probation almost never "go away" and will show up if a police officer runs your license at a stop. If you are in Washington still, your arrest and transfer back to the issuing court can take days to weeks as county jails often have to pay for transferring instate inmates. They don't rush. If you are outside Washington and Washington will not extradite you (most likely not on a misdemeanor case) you are risking harassment and scrutiny every time you have law enforcement contact. Best to contact a lawyer local to the issuing court and see if they can negotiate a way to turn yourself in with the least amount of jail time. After six years, you will need some good luck, though. Judges don't like it when people run off.

Warrants in Washington for a DUI typically last five years, but can easily be renewed upon petition of the prosecutors. I am unaware of any limit as to how many time a warrant is renewed.

A bench warrant can expire without being renewed. However, The court will typically renew warrants for DUI indefinitely. So, for all practical purposes, the answer to your question is no. Everybody gets arrested eventually. At this point, you really have 2 options. You can put together a plan to try to appease an unhappy judge and arrange to go to court to deal with this. You can also just wait until your picked up someday. Then you can face a really pissed off judge with no plan whatsoever. I know that this is scary, but you have to face it head on if you expect any favorable treatment from the judge.