> There is the flag "Clean on role recycle" for a local storage. I set this flag.
I was wrong. DiagnosticMonitor uses it's own predefined local storage, namely "DiagnosticStore":
<DefaultLocalStorage name="DiagnosticStore" sizeInMB="4096" cleanOnRoleRecycle="false"/> (this line is from one of Azure SDK files)
And the flag "cleanOnRoleRecycle" is false by default (I do not change it).
But the initial question is still actual in 2 situations:
1) A role instance is moved to a different virtual machine
2) An instance is deleted (for example when scaling down is performed)
When the instance is crashed nothing helps of course.