In my experience the WiFi works on about 75% of the equipped aircraft. And it works about 80% of the the duration of any given flight.
There is no way to predict if it is going to work other than these hints:
-seems to be better on series 800 aircraft
-fails frequently when the aircraft is turning or is in other than straight and level flight
-fails completely over some parts of the US (Mississippi/Arkansas?)
-often fails to logon to the A-list preferred free wifi, unless you are persistent and keep trying
In my experience, the wifi's performance does NOT seem to be correlated with passenger loads, time of day, day of week, etc.
Oh, and if the wifi light in the front of the cabin is going on and off, the crew is trying to reboot the system. In my experience, rebooting only fixes a problem ~ 50% of the time.
If you pay for the internet and it does not work well, complain to Southwest and they will refund your $8 without any resistance.