UPS & FedEx both go to great lengths to ensure on-time delivery, especially when it comes to air packages.
UPS & FedEx will both divert en route aircraft to other cities to pickup additional volume or otherwise begin recovery if an airplane is stuck on the ground for maintenance. FedEx will fly zigzag flights every night. Rather than go from say Fort Myers to Memphis, they'll fly mostly empty between Fort Myers up along the Florida coast, over Charlotte, then turn west over Atlanta and Birmingham before Memphis. That's so they have a plane over the appropriate markets at the appropriate times in case something goes wrong. If the plane in Charleston isn't going to make it then they can divert and get something on the ground quickly to begin recovery.
The USPS doesn't even fly...FedEx is the main air lift provider.