I have what appears to be a similar problem. This is affecting 2 of 3 MPs in my environment. The fix was to uninstall CM Client (ccmsetup /uninstall) on MP, which was causing crash of ccmexec and error 500 for MP. I'm still working with an escalation support engineer to identify root cause and a permanent fix.
If you are having the same exact issue, you might want to give this a try. Reboots is not required for uninstall or reinstall of CM Client.
You can open your MPControl.log and filter for HTTPSendRequestSync. The message repeats every 5 minutes.
Once CM Client is uninstalled, within a few minutes you should see "Call to HttpSendRequestSync succeeded for port ### with status code 200, text: OK". Wait 2 cycles (10 minutes) to verify that this resolved the issue.