From Leah Buechley...
Your creation is washable. Remove the battery and wash the garment by hand with a gentle detergent.
Note: silver coated threads will corrode over time and their resistance will gradually increase with washing and wear. To limit the effects of corrosion, insulate and protect your traces with puffy fabric paint. See my make your own electronic sewing kit page for more information. You can also revive exposed corroded traces with silver polish. Try this on a non-visible area first to see what it does to your fabric!
From Lame Lifesavers (manufacturer)...
Washing: Once you have sewn your conductive thread into clothing to create your circuit, do not worry, because Yes the thread can be washed. You may use hand or machine washing (hand washing and hang dry is best). You can wash on a warm setting, and try to use a liquid detergent to avoid any surface deposition from soaps. And NEVER use bleach. Do not get carried away with the washing however. The thread is a silver coating on a synthetic fibre, so of course, washing will degrade the integrity of the silver, over time.
While I cannot find anyone complaining about machine washing I also cannot find anyone who has actually done it. Several folks have stated they plan to do some testing but I cannot find any follow-up.
You want me to wash my wire?
I'm going to go with "no".