They're usually "blind-nailed" (using tiny brads or finishing nails with no heads, driving them in flush, then picking the fabric up with a scribe or needle to pull it clear of the heads). If you can see the brads still sticking out the back of the panel board, you may be able to tap it back down and have it hold, adding a few more blind nails to hold it firmly. Probably a better solution (or one to combine with the above) is to use an adhesive on the door frame and back side of the panel, temporarily place a clean 1"x2" vertically along the rear edge of the panel to stiffen it and either clamp or bungee cord it in place until the adhesive is set.
Hope that helps!
All the Best, Chip
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"It's wise to choose a SIX"