[Arran]

If a transistor radio is running through batteries it may need some servicing, most transistor sets use a class B audio amp, which means it shouldn't draw much current without a signal, but if there are some leaky capacitors, or drifted bias resistors, that can change. More often then not the capacitors (the electrolytic ones) will go open circuit rather then leaky, but not always, and sometimes the transistors themselves can become leaky, but usually these sorts of things result in the radio performing poorly or not at all. New caps are cheap, so I don't think I would hesitate to recap a transistor radio to get it going again, or if I wanted to use it regularly.
Regards
Arran