Some electronics won't work with rechargables as they don't like the lower voltage. With 4 batteryes your 1.2v lower (6v compared to 4.8v). Christmas eve we needed some C batteries which nothing prep/survival related takes so I don't keep spares for those. Pulled some out of the little radio/cd player my wife has in the bathtub and checked it first to make sure it worked so I assumed they were good then popped them in the to and nothing. Went to a Pharmacy that was open and bought some C cells and poppend them in and it worked fine. My older digicam is like that too, even though it came with NiMH AAA batteries I can get more pictures from lithium AA. It could just be that those radios don't like the lower voltage and think the batteries are discharged too soon. The old walkie talkies we had when I was young had two dummy batteries you placed in two of the 8 slots when you used alkaline or you could take them out and use 8 NiCad. My new walkie talkie works the same way buy it has removable packs that hold 6 and 8. Your 4 cell radios would probably last a long time if they had an extra slot to run from 5 rechargeables so the start voltages matched.
I'm still testing my new radio on rechargeables, it was designed for 8 nicads but I don't want to have to stock another type (have alk, nimh, lithium already) so for now I'm charging 8 NiMH's outside of it and topping them off monthly to take care of the self discharge. I want to do a test comparing freshly charged cells with cells that had sat for a month to see if the self discharge makes much of a difference and if the NiMH will work then bypass the simple NiCad charging circuit and buy/build an external NiMh charger,