Spring is around the corner - so decided to tend on my mower. Last
mowing season, a branch got stuck and burnt a wire. I replaced the
wire, the voltage regulator. The mower starts and runs for about 20
minutes, before dying on me. Then it will not start up because the
battery goes dead. I charge up the battery, mower starts up pretty
good - runs for 20 mins and battery is dead !!
First question is, does these mowers have charging system? Does it
seem like the charging system is bad? Or do you think there is an
electrical short? If I need to look for a short, where should I
start?

Mower is a Toro with 11HP Brigs. Battery is brand spanking new.