Would a patient benefit from continuing cognitive therapy even after solving his pathology?
No, people who have experienced some psychopathology, went into cognitive therapy and resolved their problems would most likely not benefit strongly from continuing cognitive therapy. However, they may still benefit from additional therapy in case of relapsing or future problems.
Cognitive therapy
Cognitive therapy is a short-term therapy that was designed to &quot;modify an individual's idiosyncratic, maladaptive ideation&quot; (Beck, 1970).

The basic cognitive technique consists of delineating the individual's specific misconceptions, distortions, and maladaptive assumptions, and of testing their validity and reasonableness. By loosening the grip of his perseverative, distorted ideation, the patient is enabled to formulate his experiences more realistically.

Strictly speaking, therefore, once maladaptive ideation can no longer be detected in the individual, the individual's problem is solved to the extent it can be solved, at least insofar as cognitive therapy's notion of psychopathology is concerned. This does not necessarily mean the patient is problem-free, only free of detectable problems that cognitive therapy applies to.
References

Beck, A. T. (1970). Cognitive therapy: Nature and relation to behavior therapy. Behavior therapy, 1(2), 184-200.