URL rewrite rules lost upon restart
Rather embarrassingly I have found that the issue was not related to a server restart. Instead, the loss occurred every time I published my site. I'd been setting up the rewrite directly on my server as I was unaware that the rule data is stored in the web.config file, meaning every time I'd publish my site the file would just get overwritten with my clean local copy.
To fix, I just set up the rules locally in IIS and re-published my site.