I understand that you are using a milling cutter that has a Morse 2 shank. Some of those have drawbar threads, others do not. In older days, those cutters were widely used. They certainly can fall out if there is no drawbar and there is not a very good fit up between the adapter and cutter Morse taper shanks. Did you tap the cutter into the adapter with a soft head hammer? If not, try that and see if it helps. Another thing is to lightly stone the male taper lengthwise to remove any burs. A very tiny bur can keep the entire taper from fitting correctly. I have a couple new old stock (NOS) MT3 milling cutters without drawbar threads. I do not plan to use them on my mill even though I have an adapter like you have. I am afraid I might end up with the same problem, and ruin a job. I am saving them for use in the lathe tailstock if I need a quick flat bottomed hole, used after a smaller drill bit.