This is a current limitation with Fitbit itself, every time you change your clock, you must unlock your watch face but you do not need to pay again. Please unlock your already paid watch face for free by going to this link https://kzl.io/unlock
The reason for this behavior is because when you change watch face on Fitbit, your settings and login gets wiped out, sadly this is how Fitbit designed it’s watches to work. We as developers does not have any control over it. So every time you switch your watch face on your Fitbit watch, it becomes a new installation hence you will be asked to unlock the watch face.
You can help encourage Fitbit to change this behavior, please vote on this Fitbit community thread.