My L950 often stays connected to my router, but has no internet access. When I connect via the 5GHz network, the phone indicates using the IEEE 802.11b protocoll which might be the problem.
Theses steps fixed it for me:
Force L950 to use a 2,4GHz network (do not use same SSID for 5GHz and 2,4GHz otherwise your phone will connect to wrong one!) Make sure it uses b,g or n Optional: Chosing a channel between 1 through 10