You can write a watchdog that tries to access a page on your web server and if it fails restarts the server. Run it as a scheduled task every {minute, 5 minutes, half hour, whatever...}. Implementation of this script is left as an exercise for the reader (especially on Windows, but PowerShell is probably going to be your friend).
You are however missing the Big Picture as you suspect - A failed database connection should cause your site to throw errors, but it SHOULD NOT be knocking the web server down. If this were production I would say roll out the watchdog until you can debug the problem, but since this is your development environment I would spend a day or two figuring out why a faulty DB connection is knocking the whole show down.
Bear in mind that if it's happening in development it may happen in production one day, and your employer will likely be less tolerant of the entire production environment shutting down than the developers are of the dev environment occasionally blowing up...