I'm using the perspective grid tool to help with one of my drawings, but whenever I save and close Krita, and re-open the file, the grid is no longer there, leaving me the only option to remake the grid.

Is there a way to keep the grid when I close Krita, or to have the grid become a drawing onto a layer?

No... But you can use the perspective assistant instead, which is saved with .kra files. That has all the same functionality, except for perspective correction using the clone brush.