Looped transformers compute by applying one block repeatedly, so they can run for more loops than they were trained with. Recurrent reasoners are known to overthink: iterating past the trained depth can turn a correct answer into a wrong one. Such a late error can reflect failed computation, loss of retention, or a state that later computation cannot reuse. We separate these cases in in-context Mealy-machine execution, where a simulator supplies intermediate targets and exact counterfactuals for hidden-state interventions. Models trained to answer at loop 32 are fully correct there but keep only 22% of these answers at loop 64. Retention depends on what training asks for: supervising one randomly chosen position per example, instead of always the last, keeps 99.8%, and randomizing the number of training loops also helps; truncating gradients, as in progressive training against overthinking, does not. The computation itself is exact: position $k$ is computed at loop $k$, and swapping its loop-$k$ hidden vector for the one from another input redirects every later position to that input's exact continuation (237/237 pairs in each of ten models). Retention, however, is not reuse. Even in models that keep nearly all answers, holding each position $k$ fixed from loop $k$ drops accuracy to 4--6%, whereas holding it from loop $k+4$ is harmless. A released recurrent maze network trained to avoid overthinking behaves the same way. Learning to compute is thus not learning to retain, and avoiding overthinking does not make a state reusable when its answer first appears.

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