I've unplugged it before but I don't remember if they had different heights or not. The wires don't slip either.
Maybe it was damaged while I was moving it at the back of the truck? But the header were still intact and I accidentally unplugged it and left it overnight.
If the pins are not the same height and (as it appears) there were also circumstances where physical damage could have occurred then very likely that there is damage that cannot be seen.
Could be that the plug was defective to begin with (different pin lengths or other issues) but just got jammed in when first connected.
Normal unplugging could have been problematic and a hard, accidental unplugging broke something.
The "now" being that the plug is loose, not fully connecting. May or may not be fixable.
You could try a short extension cable to secure the problem plug to an interim female port in hopes that the plug would be splinted and more secure. Then plug the other end of the extension cable in as normal.
Ensure that you get the correct extension cable with respect to pins and pin mapping.