Hi blackpearl, I am not a car stereo expert (although I've installed some) nor am I a Kenwood expert, but I am an electronics professional (technologist) so I know a thing or two about electronics. My guess is, being a two or three year old radio (I assume this because you most certainly did not just install this radio in a used car you just bought), the contacts inside the unit are defective. The (wave) soldering they do in electronics is so skimpy on sodler sometimes, you wonder how it can withstand any kind of shock.
Furthermore, my friend had a Kenwood radio, and only after a couple of years, he had a similar problem to your radio. Sure enough when I opened it up, the power/output connector was loose on every pin. Lucky for him, the sodler pads were not lifted (meaning the copper had not delaminated from the PCB) and I was able to simply resolder all the pads. the radio worked fine afterwards.
It very well could be that you have this problem in your radio.
Just open it up and look at those connections. If you can "jiggle" the connector and see the pins moving in the solder, well, you have your answer... You'll need to be technically competent to solder these back on.
You might want to use Lead-free solder as I am sure that all these consumer electroncis companies have went lead-free since about six years or so.
You can post back here with pictures if you like, I can help you determine exactly what you're looking at.
By the way, I thought the bug-eye Subarus started in 2003?