The bottom piece of our grommet die set is spring loaded. The spring depresses as the grommet is installed but pops back up.
The washer piece of the grommet should be placed over the bottom die with the barrel (stem) facing up. If the grommet is inadvertently placed upside down in the die, the sharp edge of the barrel will jam around the spring in the die. This will cause the spring to remain depressed, and the die is no longer usable.
The other possibility could be that too much pressure was applied. If there's a lot of pressure, it could actually force the barrel to get embedded in the ring and potentially come out the other end, causing it to get jammed in the die.
It doesn't always work, but you can try taking the grommet die apart and then reassembling it. For 10mm and smaller grommets, here's a quick video on how to take the bottom die apart. For larger grommets, refer to this video. Basically, you'll need to unscrew the nut at the bottom of the die to remove the internal spring, then put it back together again.
For reference, here is the proper way to install grommets using our dies: