I would think that if you started with a fully charged battery it would run for a lot longer than 20 minutes before it died - if it was simply an issue of not charging.
I'm with Dan, a good battery's not going to die that fast unless your running something else off at the same time. My little mytee pump runs the whole time so it draws. Also just because a battery is new doesn't mean it doesn't have a bad cell. I carry long battery cables just in case. Have you tried to jump it after you say the battery is dead.
Buy a meter and check to see what's really going on. It will save a lot of time and aggravation.
By the way Joseph, once the engine is running the battery is being charged, it's not running the engine. All the battery does is start It. The exception is when the charging system isn't working. You can use a meter or just disconnect the battery. If it starts acting strange then you've found your problem. The exception would be if you had a very large draw that exceeded both the charging system and battery. Then it would kill the engine. I doubt that's the case.
Ya its probably the alternator on the machine if the battery wont hold a charge.
What I find is the machine gets full and auto shuts off, guy just finish's a job and forgets to turn the key to the off position and it drains the battery. You need to jump it and run it to recharge the battery.
I abuse my battery with the water pump that's always running, a cooling fan that runs all day and an inverter running a compressor. I had to switch to a deep cycle. A regular battery just couldn't handle it. Still once the machine is running the battery isn't necessary.
Also check the harmonic balancer.. Alternator not charging the battery was one of the warning signs that the harmonic balancer needed replacing on my TM