Hi Sean,
pretty weird issue you have.
I would tend to exclude an IOS bug which shows up at the same time on 2 different switches... (but never say never).
I would first investigate about what happens at the time of the issue and before that I would like you to elaborate what you mean by 'ports dieing'. Do they go up/down? they get error-disabled? Do you see any message in the log?
Can you attach a show interface x/x (external link) and then one after the issue pops up from the 2 routers?
When you say at the same time, do you mean at the same time of the day every day (i.e. every day at 12.45pm) or simply it happens simultaneously on the 2 routers?
If it happens every day at the same time, what else occurs at that time (backups - traffic peak - SP doing something on the links etc.).
What is connected to those 2 3750s? The same SP or 2 different ones? If there are 2, are the circuits terminated to the same physical box?
As you see there are a lot of questions that might put us on the right track.
regards,
Riccardo