I’m currently taking a body shop class and we discussed burn through. As the other posts said, just re-prime and go easier on the sanding. For burn through it’s common practice to touch up the burn through with a rattle can if you only have a few small spots. BUT, TO GET PROPER ADHESION it must be the same manufacturer and type of primer.
For the work I’m doing on the bed steps of my ‘55, I was able to get the same Nason primer in both a quart and rattle can from our local Kemperle Inc distributor, for the situation that you’ve encountered.