Should punishment depreciate as time passes? As usual the answer probably depends on whether you think of punishment as justice or as a mechanism to internalize externalities.
I can see how the demands of justice could be reduced and even expire after many years pass. One view is that identity evolves and eventually the accused is a different person from the criminal of the past and justice is not served by punishing someone who is effectively a third party.
On the other hand, if the purpose is to deter crime then the passage of time should arguably increase the punishment. What matters is the perceived cost of the act evaluated at the time of acting. A fixed penalty (possibly) deferred far in the future imposes a smaller cost. To compensate for the discounting, the size of the penalty must be larger when it begins later. Its tempting to say that because the time for acting has already passed there is no retroactive incentive effect from extending the punishment. But this logic would undermine all penalties after the fact. Indeed, the incentive theory of punishment relies on prosecutors holding to their commitments presumably because of reputational concerns.
Working against this is the incentive effect on prosecutors. One reading of a statute of limitations is that it compels prosecutors to make reasonably prompt decisions to bring charges. We can model this by supposing there is a flow cost of maintaining a defense: keeping track of the whereabouts of witnesses, preserving documents, coordinating the memories of all involved. The freedom to delay induces prosecutors to optimally impose costs on the innocent in order to maximize chances of conviction.
Presumably the latter is less of a concern when the criminal has already confessed.