RE: Transmitter left on
As far as I'm aware, RC transmitters don't have any protection against the effects of the high SWR produced by an impedance mismatch through operating with the antenna retracted -- with new modules costing $25 it's just not economic to do so.
And yes, all the RF componentry likely to be damaged by running your transmitter for extended periods with the antenna down are found in the module so *if* this is the cause of your short-range, replacing the module ought to fix the problem.
Note that although it's not a legal option for US users, others elsewhere in the world can simply pop a Hitec module in their Futaba transmitter and save themselves $25. We're using the Hitec modules down here (in NZ) and they work 100%.