Assuming the horse you're looking with is high enough in the main skill of that particular comp, try filtering by highest kitty first. You can click "kitty" at the top of the column and it will change the sorting order. Rosettes usually have higher kitty comps.

Or if your horse has won a lot of rosettes already, then there's few left it hasn't won. A horse can only win the same rosette once.

Or it could also be that there aren't very many open for entries at the moment