1. make sure that you have the thread twist and the rope twist in opposite directions. Z for one, S for the other. If you are using Gutermann thread I find that Z to combine the threads into strands, and S for the second twist of strands into rope works best. Other brands might be different. This does require a 2 motor ropewalk, preferably with reversing switches on each motor.
2. check the angle of the twist. both should be approximately 45 degrees. You might need magnification to check this.
3. a dab of CA glue at the ends before cutting it free is helpful but will not overcome problems with 1. or 2.
4. Harden the rope before cutting it free. (stretch and hold it several times quite firmly. The threads will bite into each other, and tend to hold their position.)
5. If you have got the steps correct, there will be no tendency for the rope to unravel.
photo 1 explains Z and S twists. palm is up.
photo 2 shows 2 Gutermann threads before any looping (twisting)
photo 3 shows combining the threads (looping), but extra twisting is required to reach 45 degrees
photo 4 shows the finished rope with an S twist. It did not unravel.
the last 3 photos show the benefit of examining the stages with a magnifying device. (a cheap electronic microscope in my case)