I'm having similar issues with my iPhone 5 hotspot. When using the wireless on my PC, the hotspot does not appear in the list of available networks. This started when I upgraded to ios6, before that the iPhone connection was only slow to appear. Now with ios6, the connection sometimes appears after 10 or so minutes or sometimes not at all. I have the same issue trying to connect to the phones hotspot using my iPad3. The solution I found is to activate the hotspot on my iPhone and then go to the Wi-Fi menu on the iPad and select 'other' under 'Choose a Network'. I then key in my iPhone network name, security type and password. The iPad connects immediately and the PC connects within a couple of seconds. So far this has been consistant. Seems to be some issue in the wi-fi discovery process. Don't know if manually keying the wi-fi info into other devices would work, I don't have that option on my PC wireless device. Hope this helps.
I too am having this problem. It is a Verizon IPhone 5. I switched over from Android (which had a hotspot that worked great) and have had nothing but problems getting the hotspot to work. I called Verizion over the issue and they (after a long time with a Verizon rep) sent me to an Apple Specialist. They were on the phone for a while and determined that my IPhone was set up by Verizon as a IPad, causing it to have some issues with the hotspot. I was told to go to an Apple store, where they would switch the phone out for me. I did, and returned home with my shiney new IPhone (which was only a week newer than my old IPhone). When I got home I tried to use the hotspot and and found that it had the same issue. I use my hotspot almost dailey for work and am getting quite frustrated. I would switch back to Android except I am now past the date to do so without a large "early termination fee." I am considering a class action against Apple. Except for the hotspot issue I love the phone (oh yeah the maps suck too) but I am ready to give it back if they dont fix this issue ASAP. If any of you are interested let me know. Ill be suprized if this post is still here in the morning.
If your iPhone came with iOS 5 and you upgraded to iOS 6, you might try reverting to iOS 5 by re-setting the phone. My wife's phone was not upgraded to iOS 6 and has less issues with the hotspot. I'm still getting around the problem by using my iPad hotspot. I won't be upgrading that any time soon. Don't know if it's on the list of suspects but my PC WiFi is Net Gear.