The K-55V midrange driver is the Atlas PD-5VH. Those are still in production. The K-55M, however,is no longer in production and there are no parts available for it. There is a way, though, to use a K-55V (Atlas PD-5VH) diaphragm in the K-55M. ElectroVoice made the K-55M for Klipsch from about 1980 to around the year 2000. Then Klipsch went back to the still in production Atlas PD-5VH but now call it the K-55X.
The only difference between the K-55M diaphragm and the K-55V (Atlas PD-5VH) diaphragm is the diameter. The K-55V diaphragm is about 0.010 inch larger than the K-55M diaphragm.
So, here is how to make that work. Caution: This procedure requires great care because you are modifying a very delicate part, the new diaphragm. Read through this very carefully and be sure you can do this before attempting it. We at B & K Sound will be happy to do this work for you if you want to send the driver to us.
The dead K-55M. Measures open when we place an ohmmeter on the driver terminals.
Remove the 6 screws around the face.
Separate the diaphragm housing from the magnet assembly. The voice coil side of the diaphragm will now be exposed. The diaphragm is still held in place by the groove in the diaphragm housing.
Now you need to gently pry the plastic gasket off the old diaphragm. You will need to work slowly to keep from breaking the plastic gasket. It will be glued to the old diaphragm with some sticky glue.

Remove the old diaphragm. It is bad, so no special care needed in its removal.
Clean out the magnet gap. I use a folded sticky note with the sticky stuff on both sides to run around the magnet gap.
Clean the solder out of the hole in the terminal so you are ready to insert the new diaphragm's lead wire into it.
Here is a new K-55V (Atlas PD-5VH) diaphragm. Its gasket is stuck to the diaphragm with the sticky glue mentioned above.
If you try to put it the K-55M, it just will not fit. It is 0.10 inch too big.
OK, here is that delicate part. You have to remove the new diaphragm from its plastic gasket. Be very careful and take your time. The glue will release with steady pressure but too much pressure will tear the diaphragm. Just slowly work around the diaphragm until you get it loose. Careful not to stick the knife blade in too far or you will damage the voice coil.
Now, determine the positive side of the new diaphragm. There is a red dot on the diaphragm that is closest to the lead wire of the positive side. Match that dot up with the (+) terminal of the driver.
Place the new diaphragm into its groove and insert the wires through the holes you cleaned out earlier. You can solder them later.
Place the old plastic gasket over the new diaphragm. Make sure the holes in the diaphragm housing, new diaphragm and old plastic gasket all line up. you may want to use a couple of screws up through the housing to assist in the lineup. Snap the plastic gasket down inside the groove and into place.
Place the diaphragm housing back into position on the magnet assembly. Tighten the screws alternately to seat the housing back into place.
Solder the leads to the terminals and clip off the excess lead.
Check the new diaphragm. Should read about 11 ohms.