This has been a problem on the Xbox One for months now. I am not aware of any direct responses from Rebellion on this issue - very disappointing. I even emailed support directly and got no response. This was the thread I previously posted in:
Anyway, I made some progress with the 1.5.0 patch/Deathstorm 3 update. After installing the update and launching DS part 3, my map was working - this was not the case with I finished DS part 2. I did not complete the DS3 level in one session, and returned the next day. Suddenly my map had stopped working again, just like before.
I tried reloading old saves and the map refused to work (although all other controls in game were working). I then realized that I had swapped controllers because the battery had died on the first controller i started DS3 with. I plugged the original controller into the Xbox, restarted the game, and the map started working again.
I am only speculating, but it appears there is some connection between the map and the controller used to start the game/level. It does not affect anything else in the game (menus, character control, playing etc all work ok), only the map!
If you look at the original thread, I tried *everything* possible to resolve this problem, so I am not sure if what I tried on DS3 is the solution. I don't recall seeing this bug mentioned in any of the DLC patch notes, so I have no idea if the developers fixed anything.