I am not aware of a setting in SGP to trigger recovery sooner or to re-center in this scenario (that doesn't mean it's not there but I don't know about it).
Two things come to mind. First you could try increasing the size of the PHD search box. If the original star is still in that search box after 10min I think it should move the star back to the original crosshair.
Second, I know you're imaging at a modest focal length but still, 10min shouldn't be long enough to move the target that far off. Are you sure your polar alignment is good? If the target is moving halfway down the frame then I'm surprised that PHD is even able to keep up guiding under normal conditions.