Hi Pim,
Keyframes move the Balloon in the scene that its parent Null has; it is not a Simulation.
I have no idea how to keep the length of a Rope the same. I was in a more extended session with some other Master Trainers and asked, as I thought I might have missed something. The answer was that it is not a feature in the Simulation system. An indicator that it is not fully developed is perhaps that it has so far no connectors, like Springs, that I usually use for balloons and similar setups, see below (And yes, the string is behind. This needs to be baked and adjusted.
CV4_2024_drs_23_BUbr_01.c4d
I would animate the Balloon as needed and the rope's end, then connect the two. But that is just me.
All the best