I'd honestly love something like this if it actually worked the way I wanted.
I like my morning coffee, and I have a Keurig. I want to have at least one month's worth at all times. Open up that last box of 30, go ahead and order as long as it's less than 35c per pod. If the price is under 25c per pod, order enough so I have at least 120 pods (boxes of 30 = at least four full unopened boxes; if sold in packs of 100 and I still have 25 pods, then order just the one box of 100). If the price goes under 10c a pod, well, I have space in the garage, stop ordering once I have a 3 year supply AND notify me in case I want to order even more (I mean, at 10c a pod...it'll make a good Christmas present for anyone who has a Keurig, and even for those who don't once I find a cheap knock-off machine for them).
Toilet paper, I want to keep at LEAST a 6 month supply. If I open the last bulk box, order at a regular price...if the price is sky-high, I'll let the supply go down to a two month supply, at which point I'm willing to pay double per box. If the price is half-off, I mean, I'll use it anyway...feel free to buy enough to extend my stock to two years.
Same with laundry detergent, dishwasher detergent, etc. These are things that will get used anyway, I'm willing to pay a bit extra if I'm getting pretty low, but am willing to REALLY stock up if the price is low enough.
Heck, even something like boxed milk. I like to keep 3-4 weeks of milk via shelf-stable boxes (the best-by date is about 10-11 months from date of purchase, and I know they're generally good for months after the date). If there's a sale and each quart is 50cents...I'll gladly stock up a few months worth. $1...just make sure I have about a month's worth...at $2 I don't want any unless I have less than a week's worth in the pantry. More than that, powdered milk's fine.
I'm just going to guess that there's not a way to set a price you're willing to pay to restock. It's either restock at the price it costs at that exact moment, or don't use the service.