OP, I remember when I started racing I asked a similar question on a different forum. I got a reply from a guy named Bill Corliss, and I've kept it since. Posted below, with some of my own editing are thoughts on what sounds like a similar situation.
Generally a race gets a lot faster over the last few laps as everyone tries to move forward for the sprint. It sound to me like you need to work on both your speed and your ability to hold a postion in the pack near the end. It could also be that you simply don't have the makeup either physically or psychologoically to be a field sprinter, if that is the case you need to start figuring out how to get away during the race. It isn't a crime not to be able to do well in field sprints some can and some can't. Ultimately, this isn't a function of your training plan or whether or not you are "peaked" it is about knowing how to ride and race properly which you cannot get from doing intervals or following a training plan, it comes from time, experience and getting your ass kicked enough times that you start to get everything sorted out. It is possible that many of the guys who finish in front of you do so not because they are more fit but because they are better riders and know how to handle themselves in a pack sprint better than you do. Maybe find some guys who seem to do well in field sprints and ask them how they do it. Most will tell you that it is a matter of finding and following the right wheel. Generally, the same 10 guys will end up doing well in field sprints and they tend to kind of follow one another and all end up at the front at the same time. It is like a little chess game, sometimes somebody gets stuck in front at the wrong time and ends up leading things out and gets screwed and other times they hit the front at the right time and win, but it is generally the same few guys who do well in field sprints time after time. So, figure out who always seems to do well and put yourself on their wheel with about 3 to go and stay there, chances are you will do better in a sprint.
In the end, this isn't really about fitness, it is about knowing how to ride and race. You can have a motor like a Ferrari, but if you are missing the steering wheel, you are not going to get very far.
Here are a couple of cheap tips which may help your racing, then again maybe not.
1. Try to avoid pulling when you are in the field (this rule does not apply to break aways or if you are part of an organized chase). If you are in the field and are going to find yourself at the front, you have a few options. take a quick pull and out of the way or IMO, better option is to ATTACK. Stick it to someone else and make them hurt getting up to you. When you get caught, pull off. If you are pulling you are helping everyone else in the race beat YOU.
2. There are only two things you should ever be doing in the field if you are really part of the race and not just field filler. The first is ATTACKING the second is planning/getting ready to ATTACK, anything other than that and you are just along for the ride.
3. When you are racing, if you want to maintain your position in the field, for every rider you notice moving past you, figure that you have to move yourself past three other riders to hold your spot as you most likely missed at least two riders moving up.
Good luck, keep plugging along, it takes time to learn how to race. In racing once you have reached the point where you are not getting dropped from the pack the whole thing becomes less and less about fitness and more and more about smarts and skill.