Well the anemone is no more. It puffed out a milky white fluid last night which I assume is a last ditch effort at spawning before death. He was face down and inside out this morning so I flushed him.
Oh well, lesson learned. I think it was a combination of not being 100% healthy after shipping when I bought it and probably mistakes I made with my first nem (I don't know what mistakes I made, necessarily, but I'm sure there were a few.)
I won't be trying the anemone thing again until I'm in a much larger tank... It got surprisingly crowded in my tank when it would open up.