First of all let's clarify what we are talking about. In 1.0X if you lost your escape pod or got murdered in the underground you couldn't get back into the game until the next day. That isn't what death delay means. If you self destruct you can't get in that day or the next day either. This is not what death delay refers to either.
 
Death delay is a sysop configurable parameter that changes happens when your ship is destroyed and you wind up in an escape pod. If death delay is set to 0 you go about your business in the escape pod until you trade it in or lose it, just as in 1.0x. If the death delay is set to 1 and you lose your ship you will be a sitting duck in your escape pod until after midnight. If Death delay is set to 2 you will be stuck in an escape pod unable to enter the game all the way through the next day as well. The same applies to other death delay settings, you'll have to wait until midnight passes the number of times that death delay is set. Obviously, death delay can be very costly. There are two things about death delay that make it even worse:

#1 It is NOT shown on the V screen! You won't know how is set until you lose your ship or someone tells you.

#2 If your escape pod is attacked while you are "knocked out" the number of days set in the death delay will be added to your "sentence"! So if it is set to two and someone blows up your escape pod before you can get back in (a very likely occurrence) you'll have to wait ANOTHER two days before you can get back in! [boy was I ticked off when I ran afoul of this!]