My return was accepted 27 days ago, but IRS.gov shows it is still being processed. Should I be concerned? I am owed a refund.

No that's ok.  The IRS is taking a long time this year.  Everyone is waiting and asking.  Accepted only means the IRS verified some basic info on it so they know it's really from you. After it is Accepted the IRS processes it then approves it before they send the refund.