Why do I keep getting cut looking flats? My flats are causing some deep confusion. 

In the last year I've replaced at least 12 inner tubes because I keep getting flats. They are not puncture or pinch flats, they look like cuts to the tube, sometimes small incisions sometimes long gashes. They're always  the back tire on the side facing the hub and they're usually close to the valve. 

Tubes only last a couple of rides and it seems to be getting worse. I took the wheel to a shop recently hoping to gain some insight into the problem and the guy replaced the rim tape and put a new tube in and it went flat on the walk home. I tried a heavier duty 'hybrid' bike tube, and that only lasted one ride. What happens is I'll ride it once or a couple of times and either during the ride or more often at home later, after the bike has been sitting for some time, I'll hear a hissss and it's flat. When I examine the tube there's a hole that looks like a slice near the valve.

Anyone have any clue what could be going on or what to do about it? I'm thoroughly confused.Could it be a poorly designed rim? I thought it had something to do with the rim being too narrow and that putting excessive pressure on the tube. Only thing is I can't figure out why it would pop when the bike is at rest.
Is the cut always the same distance around the tube from the valve?

If so then you have something wrong in your rim.  Use the punctured tube to measure where the damage is coming from... that will give you at most two positions, one in front of the valve hole and one behind.

I think you'll find a cause in this very small sector of the rim.

BTW - had you patched your tubes rather than replacing them, the punctures might have been reduced by the extra thickness of the patch in that spot.  And if they punctured again though the patch, then you'd know straight away something's wrong there.