Been having a similar issue here with wifi. Started happening randomly after changing the theme on Sapphire 1.0 but carried over to CM6 RC3, SS 4.7 and the regular FRG01B OTA even after wiping everything clean. The wifi connected symbol stays in the status bar like it's still connected but the browser gives the "Webpage not available" message. Weird thing is I can ping the router using Terminal Emulator but can't ping google or anywhere else on the internet.
For what it's worth, it is happening to me a lot - Samsung Galaxy 3, Android 4.4.2, Verizon plan. Sometimes I get through to the website by turning off the wireless connection and going through the Verizon plan.