I have Nokia Lumia 800 with Windows Phone 7.5 and also have problems with my home wifi connection. Firstly I had an old pentagram router and couldn't to connect with it, I tried WPA, WPA 2, WEP, WPA 2 mixed or even no security, always had the same problem, shows "network don't respond".
The phone itself connects to other networks, but not my home network.
I thought that it was problem with my router (but every other device had no problems with conenction, ipad, galaxy s, laptops or even TV), so I took another router (techniklab) and I have the same problem.
On both routers in "active clients" I saw the phone when it was trying to connect, logs looks like:
Aug 20 22:13:31 wlan0: WPA2-AES PSK authentication in progress...
Aug 20 22:13:31 wlan0: A wireless client is associated - 50:2D:1D:E2:8A:87
Aug 20 22:13:31 wlan0: Open and authenticated
Aug 20 22:13:53 wlan0: A wireless client is disassociated - 50:2D:1D:E2:8A:87
Windows on my phone is up to date, router firmware also.
I can add that from couple of days I have Windows 8 (on PC) and it also cannot connect to my router, could it be some problems in new microsoft windows??