My 2021 Isuzu MU-X continually changes gears while towing a caravan

This is probably a simple case of an automatic transmission doing what it’s designed to do. In order to keep the engine in its comfort zone (and making sufficient power and torque to haul the caravan at the speed you’ve chosen) the transmission will shift through its gears to achieve that happy balance.

Any time you encounter a hill or even a headwind (and it’s more so with a heavier caravan) the transmission will assess what speed you want to hold, and then (via changing gears) keep the engine at a speed that supplies the necessary performance. Even a hot day can cause a change in the shift patterns as the transmission aims to take the strain off the cooling system by giving the engine and easier time. Again, a big, heavy caravan will amplify this effect.

However, if the transmission is changing gears for no apparent reason, then you may need to have the calibration checked and perhaps even reprogrammed. Don’t forget, though, that a modern transmission is a pretty clever piece of gear that can even choose to shift down gears going downhill to take the strain of the vehicle’s brakes. Don’t confuse an active transmission with a dud one. And if you still think the behaviour is odd, then an electronic scan of the vehicle might provide more information.