Motor won’t stay running
Do you have the vacuum advance hooked up. If you do disconnect it. Try that.
Timing could be changing when it starts.
Could it be the points are not closing at rpm speed due to a weak spring.
Disconnect the condenser you don't need it for it to run. It is only there to stop the points from getting hot over time. I have seen bad condensers do this.
Are you using a Big Block points distributor.
Post a picture of your set ip to run the engine.