Scotts by Deere S1642

[Fred from Reading]

Just bought a used Scotts S1642. It did not start when I got it. Replaced the battery cables(ugly) and the solenoid near the battery...was corroded beyond belief. Charged the battery to 12.5V on my multimeter. Wow...it started righ away. Ran terrific for 10 minutes, then sputtered and died. Could not get it to even turn starter, but heard started click. Pushed it back to garage. Battery seemed low, so recharged it. Again, after about 2 hours on the charger, it started on first try. But, again, after 10 minutes sputtered and died. Tried to save the running by adjusting the throttle choke, etc, but no engine response. And both times when it stalled, it was not under load. Just sitting and running. Now I am at a loss. I would think the engine would run well once it started and not drain the battery, but it seems this may be an electrical problem. It may need as new battery, but I hate to buy one and find this problem just reoccurs. Any advise..... ? This is my first riding lawnmower......