Strange time for an Arisaema to go dormant. It would help to know its history. Since you got it in full leaf, makes me wonder...Did it go dormant this winter? Maybe the shock of going thru the mail forced an untimely dormancy.
Does the pot have drainage holes?
Another possibility is fert burn.
And of course, there's the possibility of rot.
I would examine the corm for signs of rot if the plant continues to go downhill. If you find rot, gently cut away c a clean knife and dip in 1:10 bleach:water solution and let air dry for at least a day before replanting.
If a dormant plant fails to come back after a couple weeks, I would consider stratifying for a few wks to reawaken the corm.

Thanks for your response, Leafhead!

At this point, I'm pretty certain it's going dormant: it's doing exactly what my many Amorphophallus do when they go dormant.

I only recently learned about stratifying Arisaema corms, and I'm glad I did. Last fall, I bought some A. thunbergii var. urashima and just stored them like I do with Amorphophallus. I planted them and not only where there no signs of life after six weeks, but most of them had rotted. The two I have left are sitting in a bag in the back of my fridge for the next few weeks, and I think this new one (var. thunbergii, a gift from my sister who didn't know I already had the urashima) will join them soon. In a separate bag of course...

I have a fridge full of Milkweed seeds at the moment...
Can't plant them until middle of June sometime.