Technically, it requires a delay of 90 minutes. From the CoC --
"In the event of flight cancellation, diversion, delays of greater than 90 minutes, or delays that will cause a passenger to miss connections, Delta will (at passenger’s request) cancel the remaining ticket and refund the unused portion of the ticket and unused ancillary fees in the original form of payment in accordance with Rule 260 of these conditions of carriage. "
DL has no separate "trip-in-vain" policy that I'm aware of that would allow to cancel and refund a ticket simply because it is delayed by a few minutes.
At one point at least it was DL policy to refund if a delay caused the purpose of the trip to no longer be achievable.