How long should the auxiliary battery last in a 2010 E350? My car is 10 years old and has 37,000 miles on it.
Thanks,

If that is your factory battery - now is good time to buy lottery ticket as evidently you are in good luck.
The small batteries don't last long, but then they don't work in the car unless you have some system failure.
I use the same type of batteries in my gate opener and they barely last 2 years.

Just had the car serviced by dealership and they supposedly checked out all this stuff. Unless I am mistaken there is nothing in the Maintenance Manual about replacing the aux. battery.

From what I hear, the charging controller will let you know when it is due for replacement.
My 2014 has bigger aux battery for ECO starts and I got the message on cold mornings for several days, when ECO still did work thru the day.
Your aux battery is just emergency backup for transmission shifting, so nothing crucial.

There's some old threads which cover that battery. It's pretty cheap, about $10-$15 for an aftermarket and I believe it's an AGM so it should last pretty long. If you feel up to it, it's a cheap easy DIY if you're worried about it. Otherwise it might actually last a bit longer.

this is true. I just bought my wife an ML, and it had a "grey" battery warning light in the cluster when I bought it(and an aux battery fault code when I scanned it). I thought for sure I was going to have to replace it, but the drive from Houston to Austin must have charged it back up because it went away and has not come back. good thing I convinced the dealer to give me an extra $300 off their price to replace it before I purchased! hehehe!