Yes, they do. Some shots worse than others. If you've got field points that are fatter than the collars, that helps because they make a bigger hole. When mine get stuck, here is my process for getting them out.
1) Yank hard and fast. That gets most of them. If that doesn't work...
2) Pull up and out at about a 70 degree angle. This allows part of the collar lip to get out of the weave. If that doesn't work...
3) Push hard and then pull hard and fast. A couple times. If that doesn't work...
4) Twist the arrow CLOCKWISE while pulling outward. If that doesn't work...
5) Kick the target while simultaneously jerking the arrow out.
My Yellow Jacket target revealed a poorly epoxied HIT insert done by, presumably, a new guy at my local pro shop. I pulled the arrow and found a shiny brass insert staring at me, which I had to use vise grips to get out. Since I re-epoxied it myself I've had no issues. Also, keep in mind that I've slung a couple thousand collared shots into bag targets and I've never had to do anything destructive to the bag or arrow to get it out, even when they were really stuck. Anyone planning on epoxying their collars might consider taking a pick or toothpick and applying a hair of epoxy around the lip of the collar to act as a ramp for getting the collar out of the bag weave. I may try that with hot melt, but these collars are too expensive to me for them not to be reusable.