Hi dadsalmon
Most of the PC have one collet for the 1/2" bits and one for the 1/4" bits.
Pull the 1/4" one out all the way a take a good look at it, to make sure it's NOT damage,that's to say the collet is not cracked.
Once you have it out on the router slide a 1/4" bit into it ,if it will not just side into the collet replace it, if it sides in all the way take a look inside the router shaft for any wood chips inside the arbor, if so take a pocket knife and remove them and then take some 000 steel wool and clean out the inside then try it one more time if it still will not just slip in nice a easy replace the 1/4" collet.
Rockler will have a replacement or your in town PC server center will have one.
Bj
Just a note about over heating the bit, if you place a rubber grommet at the base of the collet nut the heat from the motor will not transfer to the router bit so to speak or the bit to the shaft it will act like a heatsink.
Definitions of heatsink
This is a device that is used to conduct heat away from its source and "spread" the heat over a larger surface area.
This will help to dissipate the energy faster, ensuring that the source of the heat is kept cooler.