From what you describe:
1) Belt is loose and slipping under load. Make sure belt is tight on motor/spindle. 1/4" depression with moderate finger pressure in the middle of the belt between motor and spindle is about right.
2) Spindle starts sticking as it warms up. If 1) above is OK, run it until it stops, then try turning spindle by hand. If it turns hard, it's sticking. Needs lube, possibly new bearings.
One of the two should resolve the problem.
Alexis de Tocqueville was a very smart man.