Starting this week, Facebook for Android stopped working while under my home network. At first I thought it was just an issue with my Access Points, and rebooted. It did not fix the problem, so I went ahead and rebooted my main router running DD-WRT. Still with the same issue, I decided to reboot the U-Verse gateway. Unfortunately nothing seemed to fix the problem.
I performed some research online and found out that by changing the MTU size of my main router, it might fix the problem. I went ahead and plugged in 1492 instead of the default 1500; done. It fixed the issue immediately.
I wonder why it started happening all of the sudden as it never gave me any problems with the MTU size of 1500 for at least a couple of years. My guess, AT&T made some changes.
Go to this link for instructions on how to get the best MTU size.