I'm sure the cells don't lose their charge, making a breeder reactor with cool down possible.The main reason people don't use them is that a reactor that's always burning hot is much, much more efficient (though I'm not sure exactly how much more so).
A cooldown breeder easiest to build and maintain of course, as you can cold-start it, and (assuming it's a Mk2) just let it run til it's out of fuel. Of course, a reactor like this is more effective the hotter it is, so it would probably make sense to make sure it's *just* about to explode when the fuel runs out. Unfortunately, that means a very long cooldown before you can safely cold-start it again. You will probably find that you need to run the reactor for 2 full cycles before the depleted cells are fully charged.
Something like this would work I think, giving you 2 fully charged cells per run, and another 4 every second run, for a total average of 4 recharged cells per run, at the cost of 2 uranium. The efficiency as you can see isn't very high.
Mark II-1 EA Positive Breeder
I'd be very interested to know how many batches of cells you could recharge in a berfect breeder, on a single cycle of uranium.