Just spitballin' here, I'd remove it and take it to an upholstery shop. Or buy some bulk mouse fur material, rip off the old fabric, and use one of those flappy sanding wheels to get rid of the old foam, and use the 3M maximum-strength spray adhesive (I think it's the stuff in the black can).

Mine is still reasonably well-attached, a few loose areas but not bad.

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