For lack of a better term, let's call the part that broke off the "handle." The above happens when the handle is sandwiched too closely to the key fob dies.
In the second photo above, only the opening of the "V" part of the hardware is sandwiched between the dies. The top part of the "V" where the handle connects doesn't touch the dies at all. This ensures that the handle won't be crushed when pressure is applied.
Tip: When using the table press with the key fob clamping dies, it's best to apply light pressure and press down only partially on one side of the hardware first. Then flip the hardware and press down a little more on the other side. Repeat. This results in more even pressure being applied to both sides of the hardware for a more uniform press, and helps to prevent over-pressing which may cause the handle to break off.