The Dor-O-Matic 1690/1790/2390 Dogging Hex Shaft is the piece that your dog key (allen wrench) fits into the lock the device in the open or dogged position. This shaft is used on the 1690, 1790, and 2390 device. The Dor-o-Matic Panic Devices have been around since the late 1960’s, but have most recently been known as the Falcon Panic Device from a name change they had in about 2008. They are basically the same device, with the same parts, just a different name plate. The part that the hex key fits into is only about 1/4" deep, because of that these tend to get rounded out, so the key will not move the shaft.
To remove the old shaft just pull with a pair of Channel Locks or Pliers. To reinstall, just press it back in to position, you might have to bend the holding tabs back down, but we very rarely have to do this. The manufacture part number on this is SHAFT.101.