It likely would die quick enough, you will not be able to build a perpetual motion machine out of yukkuri on it's own shit.
Was about to link same image. It says "nutrients were exhausted". As much as laws of common physics do not apply to magical manju, general common sense is still stating that living things need to keep intaking new digestable matter in, as daily activity or even just maintaining biological processes requires you to burn energy which you get from nutrients. Without new intake, any life form eventually dies.
Now, as I understand you are interested to theorize what may happen if you keep feeding bad memories back to it. For sake of thought experiment let's consider it is eating only it's own poo plus some small amount of bland food and water to just let it maintain body processes.
I believe that old memories would still fade over time, albeit much slower. After spending energy from initially received from food and transforming it to poo, it loses some of nutritional value. This means that over large amount of repetition almost no value will be left in poo. In image linked above it turns to sand. This probably means that at some point this is not even bean paste anymore, and therefore does not hold any memories. New memories to replace faded ones will be built in paste that resulted in digesting those small amounts of additional food. If yukkuri has no absolutely no way to fade old memories and get new ones, it dies of hunger over time, huh. That's what we get when we link memory to digesting cycle. No perpetual memory machine either.
But this way you can maybe get a yukkuri with much better capability to remember things for a long time.
Updated by EasyDeibu