Weird. Mine remembers when I turn the car off and on and even when I switch between ipod and radio but it will forget if I switch to a different playlist than the one that is currently playing with the shuffle option on. I have a V6 with base radio though, may be a difference there?
I have had this issue too, it may not be the quite the same issue your seeing. For me it depends on what Ipod I plug in and how many songs are on it. I like to keep an Ipod in each vehicle so I don't have to think about it. A 5th gen classic upgraded to 128GB with 12,000+ songs has the issue. A 5.5 classic with stock 30GB drive and 2,000+ songs works fine. The same 5.5 with a 64GB card works fine with 3-4,000 songs. The 5.5 with 128GB and 12,000+ songs forgets the shuffle. A 64GB touch (3rd gen IIRC) with 3-4,000 songs works fine.
The other thing I noticed is with 12,000+ songs Sync 3 never indexes. Even after an hour long drive I can't select a playlist. The same Ipods work fine on two different Alpine head units and playlists can be selected within a few seconds after plugging it in.
I have an android phone, but it only remembers if I haven't closed my music app. If I close it, it'll shuffle again and I generally hear some of the same songs mixed in there.
I'm talking about closing the music app in the same way an apple user would double tap the home button and see all the open apps running in the background, then able to be X'd off to close it completely. If it's still running in the background, even if not playing, it'll just pick up where the app was paused.