Signs of Failing Charging System?

[CourtLechter]

I have a 2001 GZ, and having had a ton of trouble with my battery going flat, I'm wondering if the underlying cause isn't in my charging system. What signs would I look for for a failing stator/regulator/&c?

My commute is only 5-7 miles each way and about 20 minutes, but I do spend about 10 minutes doing about 50mph, so I would think (hope?) that would be enough re-charge the discharge from starting the bike. I also take much longer (30-60min) weekend rides to go climbing.

I'm on my third battery this year, but beyond the fact that the battery needs to be replaced or recharged too often for my tastes, I've noticed that when I rev the engine the headlamp shines significantly brighter.

The final straw came this weekend when I was installing an LED-lit license plate frame. I needed to turn the bike on to test the lights (of course) several times, so I had the headlamp on without the bike running for maybe 10 minutes in total. When I put everything back together and tried to fire her up to ride back to my parking space...nothing...

So...is this normal, or should I start looking at the charging system?