Thanks Dan. I'll take the mast down early morning when the batteries are at their lowest charge and check voltage. OK, I have just read the station PDF file and see that the transmission frequency is 433Mhz, so a PCB mounted antenna is going to be too short for a quarter wave.
I have also found that the transmitter can use NiMH rechargeable batteries, but I am fairly sure that's what are currently fitted. It has been cold here for the last couple of days, but we are a bit soft when it comes to feeling the cold here in Marlborough, and count anything below 8°C as an end of species event!

But it is certainly cold enough to reduce battery efficiency. Come to think of it, I have not seen the low transmitter battery warning icon on the display, but I generally pick it up and take a battery out of the display to reset it, without studying it carefully. Hmmm now I feel embarrassed.
Your suggestion regards the transmitter is good — but the mast is located due west of the display, and being New Zealand, the solar sensor is pointed due north placing the PCB edge on to the display. I wonder if I can rotate the solar sensor relative to the battery housing? I shall try and find information about both antennas to see if I can rig something up, although I probably shouldn't need to if I get everything else right.
Thanks again for your help.