The only jump rope badge that will go through is the first one, after that Garmin for some reason doesn't count anymore to give you the other badges. I have probably recorded 50 jump rope sessions and have never gotten the one for 10 jumps, and it doesn't show me a count down to the 100 jumps.
There is no progress showing for those badges.
You can check your progress in the Progress Summary Report: https://connect.garmin.com/app/progress-summary
Select activity Jump Rope and it will show all you've logged. How many do you see there? If you don't as many as you've logged then check the activity type for the logged activities. Make sure they are logged as Jump Rope. The title is not interesting.
If you've logged Jump Rope before 2024 Feb 13 when the badges were added then you have to filter by Custom Dates and set 2024/02/13 as starting date.
I logged a quick Jump Rope activity with 300 reps now to see if there is any current issue with it, but it worked.
My count increased to 45:
Here is the logged actvivity showing the type at the top and the Jump time:
