Occasionally we get calls from customers who have experienced the loosening of our brass thumbscrews due to vibration while routing. There are several reasons why excess vibration occurs and some precautionary measures that can help eliminate the problem.
The geometry of the bit can make a huge difference with regard to vibration levels, chip removal and heat build-up (a spiral up-cut bit is generally a far better choice for mortising operations than a straight flute). Then carefully checking the flutes of the cutting tool for sharpness is a must. Spindle speed should be adjusted for the type of material being cut and the amount of material being removed (a function of depth-of-cut and bit diameter).
On a less obvious note, collets can cause more vibration problems than you might expect. When teaching routing seminars at the Woodworking Shows, I was amazed at how many woodworkers responded with blank stares when asked "how many of you have ever checked your collet for run-out?" As little as .002-.003" T.I.R. (Total Indicator Readout), can cause discernible vibration. Sometimes replacing a collet can make a world of difference without spending a lot of money.
Virtually all routing procedures produce some level of vibration, but it shouldn't be causing the brass thumbscrews to be loosening (the softer brass tightened against stainless steel creates a significant grip). If you're experiencing loosening, you might try installing an O ring or two (1/4" I.D.) under the head of the thumbscrew to absorb vibration or wrapping the thread with plumber's teflon tape. It may not eliminate your vibration, but it will most likely keep the screws from migrating out of the tool and rolling to some unseen destination on your shop's floor.