OK, this may be a longshot but I figure I will ask.
I picked up one of these http://www.amazon.com/ZyXEL-Wireless-access-point-WAP3205/dp/B002LITI7K/ref=cm_rdp_product
(although I got it for $40) and I am using it in extender mode.
I am able to set it up no problem and get devices connected to my network through it using WPA encryption. However, after being connected for about 20 minutes or so, all devices lose connection to the internet. They still see the wireless network fine, but they have no internet connection.
My router is the one that Verizon Fios gives to you. I noticed that when devices are connected via the extender, they show up as inactive on the primary router. Is it possible that this might be involved?