I've only made it twice

and that was the only times I've ever even SEEN horseradish before (or maybe noticed). Both times it was VERY hard and firm, but I don't know honestly.

Maybe you could google freshness for horseradish or something? Or maybe it will firm up?

I know I had regular radishes from my CSA that got spongey like you said, and I put in some water and they firmed and crisped right up.

Also, I still have some horseradish in my fridge leftover from months ago, and noticed it's starting to leaf out - ha!

Will see what the others say..