You must determine if when it shuts down if you are losing fuel or losing fire.
There are lots of posts here about this type problem.
Could be clogged gas cap...causing vacuum in the tank and block fuel.
It does not take 60 minutes for a mower to get hot.
Does it have a fuel filter you can see the fuel in?
you might need an in-line spark plug tester to see if it is still sparking.
You can spray starter fluid in carb when it dies and see if it starts with that...then, fuel related.
This is what I call an intermittent problem...they can be hard to track down.
Please disregard the above post.
Shifter obviously is unaware that this is a rebadged Yanmar sub-compact tractor fitted with a 3 cylinder Yanmar diesel engine.
Two things come to mind if it stops with no warning lights, provided they all light up when starting so the globes are not blown.
1) injector failures
2) lift pump failure
When cold crack the return line crank the engine and look at the fuel spewing out.
When it stops do the same.
If the lift pump is failing or the filter inside the tank is clogging there will be substantially less fuel spewing out when hot.
Do the same with all 3 injectors .
If the flow when hot is less than when cold, suspect the pump.
When was the last time the filters were changed and in particular the water drained from the filter ?
I would be inclined to drain the tank completely , rinse out, let dry then refill with known good quality fuel.
Diesel can go off real quick in hot humid weather and some will grow a fungus that looks like brownish-white jelly that clogs up everything.