I have been running in Vibrams now for quite a while (up to 8 miles at a time, at a 8:20 pace). It is almost completely painless when I don't run on roads. However, when I do, my feet hurt as though I have been standing all day or walking all day. Will this go away?
No, it will not go away. Unless you do something about it.
Since you've been running in Vibrams for "quite a while" your feet should have adapted by now, and you should be able to run without pain in your feet.
The muscles in your feet should have gained enough strength after 4-8 weeks. The joints, connective tissue, and tendons might well take longer; ½-1 year before they've adapted fully.
So if "quite a while" means a year or more then the pain in your feet will not just go away, and you'll have to change something in order to get a different result.
What you could/should do:
Barefoot running should not hurt your feet, but if it does (for an extended period of time), then something is wrong and has to be corrected. Good luck with it.