Wall plugs falling out due to crumbling plaster

Use a good quality mastic maybe Gripfill or even a resin and push the plugs into the compound after nearly filling the holes.Leave to cure which can be less than a hour depending on the mastic you choose and then offer the screws back into the plugs.

If it's a plasterboard wall, then use plasterboard toggle fixings. If it's a brick wall use window fitters self drilling screw. Drill masonry hole out and drive screw in without a wall plug. Fill the surrounding damaged area.

Are you sure this wall isn't plasterboard? The metal wall plugs you talk about are used for plasterboard. The quickest, simplest solution might be to use silicone sealant. A few beads of silicone on the back of the splash plate, push it back onto the wall and keep it held in place for a few hours (some heavy boxes pushed up against it) should do it. You could even use some silicone to fix the screws (and cover caps?) in place so that it looks as it should. Not the ideal solution I grant you, but it should work. If it is a solid wall, I would use something like gripfill to make good the crumbling walls, with a new plastic rawl plug in place. PVA the plaster first and then wait until the gripfill is fully cured before attempting to screw the splash plate back. Good luck.

if the holes arnt that bad, put the wall plugs back in and fill around with splinters of wood, when you put the screw back in it will be a tight fit if you have put in enough filling, alternativly, take away all loose plaster and fill with poly filler.

You could try to epoxy the plugs back in.