Best to cancel by 11:59 eastern. Then there is no question. The time at the departure city is supposed to govern, as I found out the hard way. Last year I bought a NW ICN-MCO-ICN ticket just after midnight central time, and went to cancel it just before 11:59 pm the next day. But of course the deadline had long since passed in Seoul. I did end up getting the refund but it took a call or two.

As far as DL goes today, I have also done the near 48 hour cancellation without a problem. Curiously, in some cases a cancel button appeared on the reservation on delta.com, and I could complete the refund processing online. In other cases, there was no button and I had to call to get the refund.