Mail shuts down unexpectedly while writing email

Safe Boot from the HD, (holding Shift key down at startup), does the problem occur in Safe Mode?

Safe mode attempts to repair Disks & clears lots of caches, so if Safe Mode works try again in regular boot.

Any change?

What exactly do you mean by "shuts down"? Does it crash or what? Perhaps more details of what happens?

Does the Connection Doctor window provide any clues?

Good luck...

No shouldn't matter, even PC keyboards work... oh, is it Wired or Bluetooth, that could be the reason, you need USB KB for problems.

Disconnect from the Internet & see if it still crashes.