The behavior of this checkbox is an action not a state.  It clears on transition from not checked to checked.  It therefore should be a button instead.

Sorry, let me try to describe it better.

When I click the checkbox labeled Clear in the serial monitor it clears the screen however if new serial is received it is displayed as normal and is not cleared.  

Clicking the checkbox again has no apparent affect.

If the intent is to clear the serial monitor buffer and screen then a button labeled Clear would be a more appropriate control.

Given your response and that you have implemented it as a checkbox, there is probably another behavior that was not apparent to me.  I just saw it as the immediate action "clear the screen" which would be better served by a button than a checkbox.

Ah.  Yes, I did notice that the serial monitor preserved the data between debug initiates.  Now I understand.  "Clear on Connect" might be a more descriptive label for the checkbox, but it's too long.  Thanks.