Ok, I've had a good look through the server and your DNN instance and it all looks very tidy.
There's nothing in the server/db or DNN instance logs to indicate this is happening. I can see carts are being created during the outage times, but whether or not that also works for customers is not clear... and I have of course seen the problem happen myself yesterday.
Your server is set to PST, but you've given the outage times in EST, so I'm going to assume the problem occurs between 12 midnight and 7am server time. That works out to 9pm to 4am my local time, so I'll check again this evening and see if I can follow the error as it happens.
Can you also pm me the host login for the DNN instance. I can view DNN logs in the db, but it's easier directly in DNN.
Regards
Rob