I told you guys a while ago that I would try to do a system reset via iTunes and luckily it would appear so far that it worked!
Yesterday I was out in the Swedish wilderness and went in and out of areas of reception and the iphone 5 connected to the network as soon as it appeared. No more disconnecting and not trying to reconnect. So the itunes reset (but first a backup of course ) is what I would suggest for whoever still has the problem.
What still bugs me though is that I cannot for the life of me figure out why this problem actually occurs? Software? Hardware? Three? Apple? Who is to blame? I don't know... Hopefully things will get better as soon as iOS 6.1 is out since Three claimed that Apple are about to fix it with a new firmware version.