I am just adding one more comment so hopefully Apple fix this issue in the next update to iOS6.
I first noticed this as to connect to my job's wifi I have to take an extra step to access it. I started to notice that after locking my iphone 5 and placing it in my pocket, leaving it there for some time and then unlocking it, it always showed LTE and never went back to wifi (unless I sign in again). This never happened with my iphone 4 with iOS5 (before somebody says that this is normal behaivor for all smartphones and iOS' versions).
I did run a ping test aswell to the IP assigned to my iphone and it consistently stopped replying after about 60 seconds (clarification: ping test was done at home where I have no issues connecting to wifi).
Agree that it is most likely a software issue but I am not sure if you are going to save battery life by stopping wifi and keeping 4G/LTE working most of the time. It will add to your monthly data usage though.