If a rare is detected while in combat, the click-target frame is prevented from showing due to limitations.
Instead of just dropping the frame entirely, how about queuing it so it shows once combat ends?

It's supposed to show after combat ends -- see the PLAYER_REGEN_ENABLED event handler here. Presumably it's not for you -- I'll see if I can reproduce that.

I've been trying to see if I could capture any errors for you by using BugSack + BugGrabber, but it doesn't throw any errors at all.

I also tried disabling all addons except for SilverDragon, and reverting to an empty profile with default settings. The issue persisted on that.