Since my 4.2.1 jailbreak (iPhone 4 - 1.59) when I wake up the phone from sleep mode WI-FI doesn't connect to my router 99% of the time. The phone sees the router but no WI-FI. Rebooting fixes it and turning WI-FI off than back on sometimes does it.
Have you tried to reset your Network Settings and also reset the Router back to default settings and redo the Router setup? This has fixed a few weird iPhone/iPad connection issues for me previously (Dlink DIR-655)
A quick google gave a few pointers but nothing that really matches your description
http://www.everythingicafe.com/forum/wifi/problem-of-iphone-with-verizon-actiontec-router-12557.html
In my case the problem was Cydia was missing my "user added" repos after the 4.2.1 upgrade/JB. This reeked all kinds of havoc with Cydia (and wi-fi). Pkgbackup didn't restore them. Once I re-added all my repos everything is working perfectly.