This sounds remarkably similar to a problem I've been chasing down for almost a year now in my 172. But I had an old generator/DC based system, and any taxiing I did that was around 5 minutes or so at low RPMs would leave the battery undercharged. I use the self serve pumps at my field, and it's about .5 mile from my hangar. I got caught a couple of times unable to re-light when I stopped to fill up the tanks after a flight. The solution was to go to an alternator, which you already have, but after I still had starting problems (slow turn over, hit the compression stroke, and that was all she wrote) I also decided to dump my Gil-25 and go to the Concorde RG-25XC. THAT was the magic bullet and it seems to have resolved everything. I don't get the chance to fly my plane as often as I like (who does?) but it can mean it will sit about two weeks between flights. I've heard that Gils are not good batteries to have if you don't fly frequently. They are mass produced to be cheap for FBOs and flight schools where planes are flown multiple times a day usually. If you don't want to dump the Gil, then you might consider a battery minder. It will keep your battery charged up and ready to go.

One thing I haven't mentioned so far is that it seems a little unusual in your case that the battery doesn't seem to be charging up during your flights. That does sound like it could be an alternator or voltage regulator problem. What is happening on your ammeter during flight? Are you getting a discharge indication? Is your battery light illuminating? They can be very dim and difficult to detect in some cases.