I've done a few click pens and dealt with a few problems, I haven't ever used that exact kit however. I'm sorry that this is so long winded, I'm just trying to describe the trouble shooting process I use.
It sounds like something is sticking. I would do this:
• Unscrew the pen in the middle
• Use your hand to push the refill in and out against the spring. Sometimes the tip of the refill is too large for the hole in the nib.
• If it sticks, remove the refill and insert it into the hole in the nib from the outside of the pen.
• If the refill sticks when inserted from the outside of the nib the hole is too small. I use a round needle file to enlarge the hole just enough to free things up.
• If the refill sticks from inside the pen barrel but not outside the there is probably glue in the tube. I would use transfer punches to remove the pen tip and coupler, clean the tube and reassemble.
• If the refill is not sticking in the lower barrel the problem is in the top of the pen. Hold the pen top and refill in your hand and operate the click mechanism.
• If the problem is in this part of the pen you will probably have to dissemble the top of the pen. This is difficult. You will probably have to use the coupler to engage the threads in the bushing and carefully work it out.
• Push the click mechanism out from the top of the pen and examine and manipulate it to locate any rough spots that may causing it to stick. I've had pens where I had to operate the mechanism several dozen times before it would behave properly.
• There is also the possibility that the pen tubes were shortened when the ends were squared. This requires that either a spacer must be fashioned or the refill shortened. I've found it difficult to make a spacer that looks good but it can be done. Shortening the refill is easy but pretty much limits the pen to a personal "user".