Hi Stacy,
Which webhook are you trying this with? Have you tried the product/update webhook?
If that doesn't work, I would recommend downloading a list of all of their products on a recurring basis and storing it in your database (/admin/products) including the inventory total available (variant, I think). Then you can run a process to find which SKUs have clients who are waiting to be notified and those with inventory > 0. Should be a pretty simple SQL query. :-)
I hope this helps.
Alex