I'm kind of guessing that you aren't getting th esoap out of system, and that it's probably built up over the years. Try running it with no soap, and no dishes inside, and use TANG where you would normally fill it with soap. the acidity in it cleans hard water stains, and it just might help clean out the tubing that is apparently not so clean. ??
I've never used a rinse aid, so I can't speak to that. Our dishwasher is 9 years old, and runs the same as it did when it was new. We do get hard water stains periodically, however, and that's how the water treatment people said to take care of it. :-)