I think that makes sense. Unfortunately, it sounds like the problem my bike had, and it means the shifter is dead. There is a slight chance you can bring them back to life with a healthy (and I mean healthy) dose of WD40 sprayed directly into the shifter.

And just to be sure, the shift levers themselves are supposed to return to their original position after every shift, but the gear will be in the newly selected gear... if they are Rapid Fire style shifters like I believe they are.