Guy,
Do check the condition of your Brick's 25 amp Fuel Injection fuse. It lives under the hood in the engine bay. Located on the driver's side clipped to a rail near the power steering reservior. There's a heavy red lead running from the battery positive terminal into one side of the holder. Follow that wire from the bat and you'll find the fuse/holder. This fuse and the holder are subject to corrosion and when they go bad the engine shuts down. I have replaced all my 240 FI fuse holders with a marine type water proof holders. I smear a little di-electric grease on the fuse legs to keep them clear of corrosion. I've had zero problems with them since.
Another sudden shut down problem I've encountered recently involved the electrical section of the ignition switch. My 88 244DL just started shutting down, the hall sender, coil and connections where all good. Often it would just start right back up. I finally I replaced the ingnition switch (two screws hold it on to the back side of the keyed lock, and there's a multi-connector that plugs into the back of the switch)After replacing the bad switch the intermitant and inexplicable shut down problem has gone away. You can buy new switches from FCP Groton (http://www.fcpgroton.com/volvo.htm) or Import Parts Specialists (http://www.ips-parts.com/) for 35-80 bucks. I used a switch from a low miles wreck @ my local Pick and Pull. $10. As I recall any 240 switch from 75-89 will work in all of those 240 model years. Hope this helps.