It’s not going to be a fuse. You’d have other symptoms. Besides, you could very easily check that yourself.I've got the 3.6. My stop/start feature stopped working a while ago. Most people aren't crazy about that feature so I never brought it into the dealership to get it looked at. I am still under warranty. I have read that it's typically a blown fuse that causes this, or maybe an auxiliary battery problem that prevents it from working properly. I'll have it looked at during my next oil change as my warranty is up in 3 months. So if it is a battery issue, that could lend some evidence to support your theory.
Word of caution: this dumb design has the batteries wired in parallel when the ignition is off. That means if your little battery has a bad cell, for example, it’s going to draw down your main. Assuming you can still start up the next day, your alternator is going to do it’s best to bring the charge back up, but will be fighting a losing battle. That’s exactly what happened to me. Dealer replaced the little one and said the big one was fine... it wasn’t, perhaps because the bad little one kept drawing from it thereby shortening its life, or perhaps because the batteries they use are cheap junk.
Anyway, do consider bypassing that sucker after they give you a new one under warranty.
Tip: most shops are too busy to test batteries. If you go in with good info, chances are they’ll take your word for it and just slap in a new battery.