Sounds like the cap isn't fully seating on the nipple. Reduce the diameter of the nipple. There are several methods.
1. File it down by hand, keeping it a round as possible.
2. Use a 1/4" wide strip of emory paper about ten inches long to sand the sides, kind of like polishing the toe of your shoe with a cloth.
3. Chuck the nipple in a power drill or drill press and file it down as it rotates.
You won't have to take it down much for the cap to fit, so go slowly and check often by trying a cap on it.
As an alternative (or to check to see if cap fit is actually the problem) place a cap on your nipple the way you normally would, then lower your hammer and push down on the hammer to seat the cap all of the way.