my second NEW iphone 4s keeps switching itself off Help

i had an iphone 3 and it was fine and had no problems.  i upgraded to a new 4s and have had hassles ever since!  it kept switching off and would only restart when i held down the power and home buttons... and this was happening half a dozen times a day at first.

i restored it several times and couldn't get it to work so rang apple tech support.  they got me to go through a few things and then decided it was a hardware issue so suggested i take it back to the point of purchase and get a new one, which i did.  but i am still having the same problems!  so i can't imagine that it is a hardware problem.  how likely is it that i get TWO new phones and they both have the same problem??!!

So...

have tried another restore

have made sure software is up to date

have got a new cover (wasn't confident with this, but someone told me it worked for their signal, so thought it was worth a try)

have tried reducing the load - it is 8G and was pretty full so took out quite a few songs, etc

have been checking to make sure not too many applications open at once

have started using a password, as sometimes it will restart and then do something weird, like take a photo!

have tried taking out sim card whilst phone on and then reinstalling.  someone suggested this to me and it seemed to work for a while.  it certainly improved and was only happening maybe once every day or two, instead of several times a day.

has now started to happen more and more often.  very frustrating as i am now obsessing and keep checking to make sure it is still on as I keep thinking it might be off...

i don't live in a city so it is not easy to go to an apple store.  even when they got me the new one it took 3 weeks which was extreeeemely frustrating as had to use an old nokia at the time so lost all my appointments, reminders, etc.

does anyone at all have any idea what might be wrong ?  I will love you forever

thanks