Presumably when the transmitter tells you so!
As far as I am aware, virtually every piece of electronic equipment has a minimum voltage. 4 NiMh cells have a nominal voltage of 4.8 volts and 4 Alkaline dry cells have nominal voltage of 6 volts, If Joysway say that rechargeables should not be used, one can probably assume that they consider the voltage from rechargeables to be inadequate.
I would suggest you take the batteries out of the transmitter and put them in another of your Joysway transmitters. If that beeps too, then I think it fair to assume the batteries need replacing.
For the cost of a set of batteries and the length of time they last, I would just change them and get on with sailing. You could, of course, just keep using them and see how long it takes to sail off into the sunset under its own control and then you would know for sure whether the beeping was relevant or not!
David