I had same issue
The collet that came with router was not an issue
I got the precision ones and had issues with the tools coming lose, especially when using a down cut
I got over it by not pushing the tool too far into the collet seems like the collet squeezes better onto the tool
I also had problems, made several changes and something in this mix worked for me.
Whenever I change bits, I take the old one out then use my dust collection hose to suck out/clean the collect (while it is still in the router). I started doing this when I noticed the quantity of dust that builds up within and on top of the collect. Enough dust that it was possible I was not getting the clamping force I needed because of the dust filled into the gaps.
I retired a 1/8th collet after I mistakenly used it to clamp a metric bit. I blamed myself for over squeezed it, and decided it was better to punish my credit card rather than risk future bit slipping.
I switched to Elair Collects but I don’t really think they are better… just took the mindset that these wear out just like bits do.
@WillAdams once used the phase “monkey tight, not gorilla tight” when describing clamping bits within collets and that just kind-of stuck in my head.
when I change bits of any length, when inserting into the collet I hold the bit about .75, or a little less for .125 bits from the end, and allow my fingers be the stopping point.