A few thoughts and suggestions;
Get the model and serial numbers from the machine, go to the Scag website, on left side click on manuals, the wiring diagrams are in the operators manuals.
When you say running, is this with the PTO switch in the on position, the deck turning and the travel levers pulled in????
With many machines to include my Tiger Cub, I have had to disconnect and clean the electrical connectors.
Have you checked the electric clutch for continuity and shorting??
Check the path of the clutch wiring harness as it is close to the belts.
What is the charging system voltage? What does this voltage do while the machine is in operation as time gets close to the fuse blowing?
Check the grounds that are connected to the engine mounting bolt.
Condition of the fuse holder itself?
Chaffing wires?
Key switch?
All battery power comes from the battery side of the start solenoid, to the engine harness adapter, to the 20 amp fuse, to the B terminal on the key switch. It also splits off to the start circuit relay that is usually mounted under the same panel with the key switch and the PTO switch.
Basicly when the engine is running, PTO on, deck turning, the major player in the system that draws amperage is the electrical clutch. I have had PTO switches and key switches give me grief at times.
Mad Mackie in CT