If this is a new router, perhaps it is possible that you have a defective machine with a damaged collet, or a piece of debris is jammed in the collet. If you have only observed this on a single bit it's also possible that your bit has a defective shank or another quality issue.
Be sure to also obey the minimum insertion depth marking on your bit if it has one (or insert it all the way and then pull out maybe 1/8" tops if it doesn't).
Be sure you are using the correct size as well, e.g. don't use a 6mm bit in a 1/4" collet.
Your collet should be locking your bit in place, even without you having to crank as hard as you can when tightening it.