hy
on one side, maybe the tool is pushed too much, or maybe there is something not so rigid about the fixture or spindle or the tool itself
on the other side, they need to sale, and quality sometimes may be compromised, even if the product video shows promising
a high-feed mill handles forces and frequencies > than same size end mill, simply because it is built for mrr+
is not cost efective to use an integral tool, so using inserts means lower cost; but, just to show something, imagine an integral tool : it has no screws down there, and it is being secured in a toolholder, with a big screw ( or maybe 2, etc ), and those screws are located close to spindle face : so, they are bigger, more resistant, and the cutting forces/reactions that reach them, are being dumped along the way by the toolholder, and the screw itself, being near the spindle, is in a more rigid area
thus, those tiny screws that hold the insert, are in the war zone
a small threaded ansamble can not deal with stress as ok as a biiger one, and also, the mill insert is subject to more contacts with the material, because it is making and losing contact at each spindle revolution, while on a lathe, things are different :thus, in other words, same screw for a similar insert, on a lathe toolholder, won't come loose as fast as on the mill
what to do ?
you may scan the market, and try products until something happens ( like you get lucky, or bored, or both )
decrease the diameter of current tools; it should hang on better, as long as screws size is identical, but is not a must, because a smaller tool with similar screws, may have a shorter id thread
use secure paste, like locktite, or how is it calledd ? but the drawback, is that it will require more force to unscrew the tiny screw, and his head may get damaged
can craft your own milling head; here are some tips :
... must be heavy/heat treat for high forces(mrr+), or light for high rpms(mrr-)
... besides the middle screw, consider a 2nd clamp, or entirely redesign the insert bed
... the more rigid the insert clamp it, the less inserts you will be able to mount on it
if you have experimented enough inserts, chose those ones that you like, and for them, start creating a milling head; an y lathe will make this job easier
if you wish, i will help you / kindly