I have a 2013 LS in which I leave my iPod plugged in all the time. It usually plays perfectly. However, it frequently loses connection for no apparent reason and the audio shuts off. When I turn the audio back on the iPod is not shown on the menu. I have to dig it out of the console and remove and reinsert the plug. The iPod then shows up on the menu and all is well for a while.
Has anyone else experienced this?

 

Sounds similar to what happens when connected to a computer. Bad cable maybe? Also, some cables can easily come partially unplugged at the 30 pin connector on the player. Maybe a reset on the iPod will fix it. There is a way (don't remember how) to do it without losing your music.

I have only had my (2011) LS for just over a month but my iPod Classic plays every time.

 

It's software related. I've had this happen with mine on several different vehicles. I think the unit runs the battery down intentionally every now and again and when it does that, it starts working fine next time I turn the car on. Probably because it is now recharging again .