550 Second pinion friction spring damage?

Archer

You don't oil this spot - it is left dry.

I often see these springs damaged because someone didn't protect them when they pressed the sweep seconds hand in place. This is a damaged one beside a new one:

To prevent these from getting damaged, I was taught in school that you should place a piece of old mainspring between the pinion and the spring, like this:

This keeps the spring from being pressed into the shape of the end of the sweep seconds pinion, like yours has been. I can't say that this is the source of your intermittent stopping issue, but it can lead to erratic movement of the sweep seconds hand. This erratic movement then leads whoever is working on the watch to make the spring apply more force in order to stop the erratic movement, leading to lower balance amplitudes.

Your doesn;t look too damaged really, so you may be able to carefully flatten it out, but if not then a replacement may be needed. But I would also check the tension - it just needs to be enough that the seconds hand doesn't flutter when moving around the dial - test this by holding the watch vertically with 6 to the ground and 12 to the sky, and watch for stuttering as the hand moves from 12 to 6 (you won't see it when the hand is moving "uphill").

sheepdoll

I always find it a bonus when a junked plate, like the one I got last week still has this attached.

I made some custom laser etched fixtures, with a setscrew to press against the spring.

I like to keep extras of these around. Just in case one does what @ErichKeane did. Or they break in half when the pinion presses through.

Pinions are the bane though of this design. Never seem to be the correct height. They also tend to trend high in listings.