Tape as suggested, or wrap in string/thread and CA it. Small string is what I use and it adds considerable strength. Turn it to get it off with your favorite chisel.
I had one that separated after I had cut down through the string and had it rounded over. I was fortunate to be able to re-align everything perfectly and re-glue it.
At this point, I used rubber bands doubled and trippled over on both ends of the same blank and turned one end down to about 2 mm from the correct size, add rubber bands to that end and turn the other end down. At this point I join my friend Mr. Patience and sand the last 2 millimeters. Takes a lot of work and time, but it works for me.
OH, I forgot to say that (above) my pen segments and separation was horizontal.
For round segments as in brass or aluminum washer shaped, I had one of those come loose only once but I saw it happening and knew what the problem was - heat. Preventing heat build up will usually allow the strength of CA or epoxy to keep its strength. Take small bites and move away, let it sit a minute or so and then do another run.