Programming left-click and right-click on unit frames for anything other than their default UI behavior is a very bad idea -- left click is used to set that unit frame to the current target and right-click is used to open the menu for that unit frame.
I suspect that when the UI is reloaded, the unit frames are always resetting to the default unit frame behavior... that's hard coded into the creation of a unit frame. I'm not sure if Clique is overriding that, but I'm betting it does not which would explain the problem you're having.
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