I seem to be staying connected when plugged in directly through the modem.
Why you might not be on FIOS, I point to http://forums.verizon.com/t5/FiOS-Internet/Why-your-Wi-Fi-is-slow/td-p/534451
Since you've identified that the problem is with WiFi, get a copy of inSSider and use it to figure out what other WiFi networks are in your area. Use it to find a WiFi channel that isn't too crowded (1, 6, or 11). Then, set your router to use that channel.
You can also consider purchasing a dual-band router. 5Ghz isn't as crowded as 2.4GHz. Be sure to check that your devices are dual band before going this route.
Good luck.
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