Follow up from my Pinterest board This I will try and let you know how it turns out:
Regrowing celery for me has been a bust. I have tried low sun, bright sun, inside and out without with the same results. As you can see, the plant continues to grow, but the stalks are very thin and consistently die off as new stalks emerge. I tried never letting the dirt dry out and letting the dirt dry out between watering The dirt was new dirt from bag of potting soil, so I don't think that poor soil was the problem either. Anyway, this was a "busted" for me. It would be interesting to see if re-growing celery resulted in edible produce for anyone else and how they made it happen.
The original pinned post can be see here: Chickensintheroad.com Even though this didn't work out for me, I'd still recommend taking a look at their site - good info to be had.