Has anyone pointed out vibration as to being a factor
I'd like to agree it's more that likely down to vibration, and would point in the direction of the main shaft being out of kilter and unbalanced, or maybe its those shaft bearings that are now wearing out. OP hasn't stated the width of the cut, but i would say even 3mx12.7mm is not going to cause such a vibration as to have the cutter move in the collet. Unless of course the threads on the shaft and nut are worn and there's just no room to tighten it any further, or the OP is not tightening it properly but if thase factors arent a factor, then vibration is likely from the machine. And there's a reason it's only forty quid.Moving against the rotation of the bit. It causes more vibration and high loads on the bit. A but of grease or dirt in the collet along with climb cutting can pull the bit out. As I've just realized you are cutting a rebate, so yes, half your cut is climb cutting. Not the routers fault im afraid.