GE Profile Harmony Top Load Washer - Won't drain
After more thought, it dawned on me another possible reason. In my case, the washer is draining water, but it keeps cycling the pump on and off, thinking that the pump isn't working properly, and the washer doesn't go into its high-speed spin to eke the last bit of water out. It dawned on me that it could be that the pump is fine, but the sensor is lying, saying there is more water when there isn't.
I looked at the tube for the sensor, and noticed a small blockage of white soft stuff. I disconnected the sensor tube from the tub (in the back), managed to squeeze the blockage out, connected it back up, and now it all works fine (about 5 loads and I haven't seen the pump message)!
So if your pump is draining water successfully, but the washer keeps complaining and refuses to go into the high-speed spin, then perhaps this is your situation as well (or a bad sensor, etc.).
Note that I'm pretty sure the blockage is what ended up ruining my first pump. The blockage matches the color and consistency of the caulk/glue that was used to attach the sensor tube, so my suspicion is that too much was put on at the factory and ended up going into the tube, but not enough to cause problems initially. After several years of use and perhaps a bit of water mineral buildup, it finally became a full clog.
Finally, note that, as you may have guessed from the design of the machine, when you disconnect the hoses at the bottom, there's always a few cups or more of water in the two black hoses and the pump that it can't manage to push all the way to the drain.