Depends on the age of the router too. How often the firmware is updated, etc. A reboot of the router may in fact apply a firmware update that plays nice with the iphone 5.
I dont think you get it.
Its not a router issue or that the router needs an update.
My phone does the same in 4-5 different routers in both open and password protected wifi's. Brand new routers and older and others that I have no idea what they are cause I cant see them like at starbucks, Mcdonalds and other public wifi's.
Every other device like laptops, PS3, nintendo Wii, iphone 4, Tivo DVR box etc.. all connect and work fine but the i5.
You still dont understand that its a widespread problem with many iphone 5's and well documented? That's the reason Apple put out 6.0.2 just for the iphone 5 but it didnt fix anything. Still the same.
Im getting sick of having to restart my iphone 5 about 8-10 times a day to be able to use wifi. And Im affraid if I exchange it I will just get a replacement with the same problems like many others did already.
This is a hardware issue Apple needs to address and hope later iphone 5 models will have a different chip that will work with every router out there like every wifi device should be able to do out of the box.