Can Self-Improving Agents Retain the Ability to Improve?

Can a system retain a learned way to improve after adapting to other domains? Stable search outcomes alone are insufficient: a fallback can sustain performance, or the proposer may never have acquired an advantage. We distinguish task, updater, and proposer competence, and require acquisition, probe sensitivity, and exercised interference before interpreting retention. Three controlled experiments train a contextual selector over 24 classifiers on three real datasets, using 51,840 fits and separate development and assessment pools. The proposer gains 3.550 balanced-accuracy percentage points over uniform selection (95% interval [3.413,3.677]). Subsequent adaptation improves the aggregate score by 0.141 points, although Digits loses 0.229 points. Reservoir replay reduces the aggregate retention change by 0.161 points. Changing the search probe also changes the aggregate retention estimate's sign. These results support a diagnostic approach to retained improvement ability in finite algorithm selection; the externally fixed learning rule does not demonstrate recursive self-modification.