Always, always check your spark First. Verify that you have a bright, bluish white spark that will jump at least 5/16". Only then go on to fuel.
Take an old spark plug and stretch the electrodes to about 5/16" . Hook it to a plug wire and lay it on the head somewhere where it is grounded and watch your spark. Post back with your findings.
Also let us know if you have a front mount or side mount distributer and whether your N is 6 or 12 volts.

 

Thanks,
So all of the plugs fire a good spark. But would I need to check that the moment it dies, how could I go about that?

The tractor has a front mount distributor and it’s been converted to 12V (the ground is on the positive terminal and the hot is on the negative terminal but it works is this normal?)

 

Just checked the distributor and noticed it had some debris in there and what looked like metal shavings. I cleaned it out but still having the issue. Would replacing the cap be a good idea at this point?

Also, is there a way to check if the coil is the problem now? I replaced the coil a couple years ago and the condenser a year ago.

 

Try a new capacitor. If it doesn't help try another one. They don't make em like they used to.

 

Do or did you check the spark right after it quit ??
A bad coil will run after it cools enough and start back up
so git a wide gap plug like UD said and a wrench in yer pocket and test it right when it quits not after ya run to the shed for the plug and wrench.
BTDT meself, found the bad coil and replaced it YMMV, also check yer fuel flow, open the bottom plug on yer carb and let it flow you should git a pint in a couple minutes if not clean yer carb, fuel line and screens ....