I have had this happen to me. It is when the screw which locates on the thing that pops it up comes loose and unscrews a bit and then gets a bit off centre and jams it.
I doubt very much if a magnet would be of any use as these plugs tend to be of Chrome plated brass or other non ferrous cast metal.
Emptying the batch with a jug is a sound idea as it reduces the pressure on the plug.
If you go to a proper car shop such as a motor factor you can buy a tool for grinding car engine valves in. All it is , is a wooden stick with a small strong rubber sucker at each end. Stick that onto your plug and it will pull out. Then you can then adjust your screw length.
Simples!