After sitting for a month unused, my battery charge is too low to turn the engine over. The Bentley manual says to remove the battery from the car to recharge it with an external charger.
Is this really necessary? I'll lose any fault codes stored in the system if i disconnect the battery. If you can jump start it using the terminal in the engine compartment (Cooper S), why can't you attach a charger to that same terminal, or directly to the battery, and trickle-charge the battery?

 

You wont lose fault codes when disconnecting the battery. They are stored in nonvolatile RAM. The radio stations will still be intact as well. The only thing you will lose is the clock settings.

There is no reason you cannot use a modern batery charger with the battery still in the vehicle. These chargers unclude regulation circuitry that prevents the voltage applied to the battery (and the car's electrical system) from going beyond 16 volts. Older, brute force-style chargers had no such protection and can cause damage or issues with the vehicle's electronics. Also, the old style transformer-and-rectifier chargers would feed pulsating DC into the system and can confuse or damage electronics when used on a deeply discharged or defective battery. This can happen because such a battery does not have in it the capacity to 'buffer' electrical impulses.

If your battery is the original OEM one that came with the car, it's most likely worn out and this will be a continuing process of discovering a dead battery when the car sits. Charging helps in the short term, but it will reach a point where the battery will peter out while the car is parked for a short period of time, such as when at work. I recommend that you pick up a new battery soon to head off such circumstances.

In the meantime, if your charger is a 'trickle' charger and is no more than, or has settings for no more than 2 amps, it should be safe to use it at that setting with the battery in the car and connected.