You could you use the Rules module, and set up a rule that re-enables comments after x amount of time.
- Install Rules
- Create a new rule
- When you get to midnight (or whenever), then enable comments on posts that have comments disabled.
There's not really much more I can say. The Rules module is really self explanatory when you create a new one.
The only issue you may have is whether or not Rules has the option of enabling comments. If it doesn't, then you're looking at creating a custom module that hooks into Cron.