The three most common reasons for this are (in order):
1) improper loading, something is being loaded that is either restricting the spring action of the detergent cup door from opening or blocking the spray flow from the lower arm from completely flushing the cup when opened. Review the owners manual section on proper dishwasher loading.
2) The inlet water temperature is not hot enough. Check your water heater settings, and run the hot water at the sink until hot before starting the dishwsher (check temperature of the inlet water). If necessary use the temperature boost option (if available).
3) Parts failure. Could be the inlet solenoid has failed (due to scale or less than adeqate water pressure) or a pump failure.
Other possibilities include that the water level sensor is not working, the tub is not level, or the drain screen is clogged, preventing full draining of the DW.
If I were you I'd also double check there isn't a silent recall on your dishwasher with GE. They have had over a millon DW recalled since 2004, however there are also quite a few that are under a silent recall - having issues that are not unlike what you describe. With the limited warranty still covering some of what you describe, If I were you, I'd call their toll-free number and discuss with them, as well as look into the easy consumer check-trouble shooting I've mentioned.
Also, you're going to need to know something about your water quality. In most cases one does not need to use as much automatic DW detergent (often less than half of what the average consumer loads).
It wouldn't hurt to run a few cycles of the DW empty starting with 2 cups of Distilled white vinegar, followed with 2 cycles using just one cup of vinegar in each load. Also cleaning up the detergent cup hinge, door, and resevoir.
Finally, if you use a wooden slat in the door slat you can check the inlet water pressure during the fill cycle - and the incoming temperature. If it is merely a trickle, I'd suspect the solenoid and/or a restriction in the inlet valve or piping.
Finally, if your discharge hose isn't hung/looped properly it can cause similar problems eventually.