This also happens with the first version basic probe, with the rocket engines on top.

Also happens for me on the zero G probe... Falls off immediately during "launch". Didn't do it for my first rover, but has continued to do it consistently since I first noticed it.

Edit: just tried going to a save prior to when i first noticed this happen, and it works fine. exact same craft. something about game state causing this, perhaps?

Double Edit: And then, during that same test launch, it fell off again as soon as I applied any amount of roll to the craft.

Final Edit: I turned down the Physics Quality setting all the way, and suddenly it became (at the very least) more stable. the part jiggled all the way down to the ground, but by turning off auto-kill-translate and throttling it myself gently, I was able to descend intact.