They don't click back to off once I have turned.
I have a 2009 G6 that's having the same problem. It started out where once in a while the turn signal wouldn't cancel itself automatically like it should, but its to the point now where its more often than not. Mine does it far worse when turning right than left.
I think a trip to the dealer is in order to get it fixed. Until recently the trip to the dealer seemed like it was more trouble than the problem was, but its starting to get annoying now so I think its dealer time soon.
2009 Pontiac G6 Sedan - Ecotec 2.4L I4, 6-speed Auto, Sun & Sound, Performance Red, 15k miles.
2002 GMC Envoy SLE - Vortec 4.2L I6, 2WD, 3.42, G80, T/C, Indigo Blue Metallic, 125,000 miles.