I think it's highly variable as to how much needs to be ground off. Sometimes, and actually I think most of the time, just two or three light sharpenings will bring an improvement in edge stability.
I did have a lesson in patience with one inexpensive paring knife, years ago. I'd resharpened it multiple times over the span of weeks, or even months, and the edge would simply crumble away as soon as it was apexed. It wouldn't form an obvious burr, but instead would just crumble into dust when the edge was thinned past a certain point. I was tempted to assume it was completely worthless and just throw it away. But instead, I just put it away and forget about it for some time, until I was willing to have another go at it. After months of that approach, it finally took a decent edge that held up as I'd expect for simple kitchen stainless steel, and became a pleasure to use in the kitchen.
I'd not grind too much off at once though. I think the safest approach is just to take a little at a time, each time you tune up the edge. Most of the time, that has worked for me and it doesn't take too long to get the edge as stable as it should be. I think most heat-damaged edges are probably only lightly burned (not discolored, but weakened) very near to the factory apex. So in my experience, it usually doesn't take much to remove that damaged steel near the edge.