Google Chrome's webkitGetUserMedia - what if the user ignores the dialog?
It seems that this is a known bug.
Issue 252904: Infobar popup on mic/cam permission results in unexpected permission state; causes unrecoverable lack of permission on reload
There are currently two patches in the comment thread on that bug, so at least you know they are working to fix the issue. Unfortunately there don't appear to be any real workarounds for the bug in the mean time.
One thing worth mentioning: if you close the tab and then reopen the url, that does seem to force the permission dialog to show again. I know that's not a real solution, but at least it's better than closing the whole browser (which I think is what you've been doing up to now).