A portmanteau of admiration and sympathy. The particular feeling workaholics try to inspire in others for their intense dedication and intense servitude.
Me: Joan spent twenty minutes telling me how hard and how long she works each day at XYZ Imports. Her dedication is admirable, but I feel sorry for her at the same time. It sounds miserable.
You: Ah, you feel admirampathy towards her.
Me: Totally!