I'm not sure that's true. Lots of people play games where their rankings shift down if they don't constantly play. In a lot of cases, this actually increases engagement. I think we would need to see some evidence here, but the null hypothesis should be that user engagement does not change.
If one wanted to assume that it does negatively effect engagement, however, then maybe an extended approach then is to show the ranking of the user's ratio score? This is less of a judgement of their score and more of a pleasant reminder that they are not contributing as much as others. Alternatively, you could also set the risk-free-rate to 0 for both the comment and day, then only update the scores periodically.
I suppose one could argue that it's not a competition and you shouldn't be vying for a higher score, but then why show us our karma at all? Similarly, if one believes that consistent contribution is not important to the community, then it's a philosophical difference and we'll have to agree to disagree there.