It may seem like an obvious question, but are you trimming the cases?
If the cases are too long, the mouth will jam in the rifling. This can lead to failure to chamber. It can also lead to dangerous overpressure if the round does chamber (as the rifling "crimps" the case mouth).
Also, "darn close" is relative. The difference between headspace GO and NOGO for many calibers is only 0.006", and sometimes less.
If your resized cases aren't 0.003" less than the fired cases (using your headspace comparator), you can have chambering problems.
.30-06 Springfield: 100 yrs + and still going strong