Should I replace my magnetron? Is there anything else upstream of the mode stirrer?
Somewhere on the magnetron is a thermal fuse or cutoff. When the magnetron gets to hot, it shuts off power to the device. Some of these fuses reset once the device cools, some don't. Sounds like you have one of the later. You can replace the fuse, temp rating is usually written on the device itself.
While you're in there, clean the cooling fins on your magnetron with 409 or similar cleaner and a toothbrush. Buildup of kitchen grease on them can make the magnetron run too hot. Also check that the cooling fan, if any, is working, has a free air path, and is pointed at the magnetron fins.
When my microwave started cutting out, all it took was a good magnetron cleaning to get it running again. Sounds like your thermal fuse is a one-shot though. You might replace it with a auto-reset version.