My Babylock won't cut the thread unless the foot is down, and the only time it comes unthreaded is if I use specific brands of threads. Other specific brands of thread work fine every time. So I'm guessing your machine is fussy about brands of thread, and there should be brands which do not unthread. Experiment with a variety of brands of thread. For me Gutterman thread works great, as do some others.

My Ellisimo raises the presser foot automatically after the cutter cuts the thread. I've never had a problem with the needle comim-ng unthreaded.