Davey, there's an issue with the older style extractor that causes it to not remove the spent round just like the old spring driven ejector, but for different a reason.
You need to understand there is no new ejector, only the old ejector that was spring driven and throws the case out of the chamber. Then they went to extractors that don't throw the case out. Then they changed the extractor style to a more reliable mechanism probably because they had trouble like you mention. If you have the early style extractor, it probably needs to be fixed by the factory. You didn't say which yours does with the empty. throw it out or you have to pick it out?
If your underlug looks like the one on top in the pic below with the staked screwhead, that's the one that is the problem child, the other one is an old ejector type that most everyone loves.
As everyone has stated, it must be clean to begin with, that includes before shooting and also after using the polish.
Besides the dirty chamber or extractor/ejector, there also may be a problem with the chamber itself that is causing the problem, if you get it cleaned good and it's still a problem, you need to contact H&R after New Years at their toll free number in the FAQs and ask them to fix it, also ask that they pay for shipping while you're at it.

Also, if the trigger is too heavy, have em do a 3-4lb trigger job on it. If you're interested in an extra barrel or 3, that would be a good time too!! Just some things to consider now instead of after the fact.
Tim
