Car starts right up after storage...but....

Check the coil.
Coils hate heat of any kind, and so do ballast resistors too.
Is it points or electronic ignition?
If points, it could be the condenser. If electronic, it could be the coil, ballast resistor, or the control box.
Control boxes and ballast resistors usually just fail and that's it, it won't start.
Also check for loose wires (especially grounds) and wires partially chewed out by rodents.
If the coil is HOT when you touch it, it is going bad, or is bad.
My money is on the coil going dead when warm, too much resistance.