Power Source — depends on how much of it is electronic. An EMP destroys electronics (semiconductors). EMP shielding is designed to protect the electronics.
Also, maybe it is less important to be able to continue fighting and more important to be able to limp back to base for repairs. Although being able to fight would be useful as a defensive measure as you return to base (while the enemy is shooting at you.
The A10 is a good example of designed in redundancy survivability.
Didn’t you say:
“Nothing is EMP proof. Only resistant to EMP.” the only power source i can think of that would be EMP proof would be a steam engine.