This is my issue as well. I dropped the quest thinking i could just pick it up back....wrong.

I had to reselect the runes to get it to unlock.

I had something weird happen in my quest. I did all the requirements, and actually started the exotic mission. Well stupid me decided to start it 1/2 hour before I had to leave for work, so I got to where I had to do all the jumping to find the 3 hidden crystals and decided well i better stop or else I'll be late to work, so I bailed. When I got home I went in through the quest icon on the lost city map. I saw i had to start from the very beginning and said screw this I'll do it later. I went to the slab and set up the ruins for a nether run, and turned off the scotopic rune. I did the nether, then went back to the exotic mission and poof, no more icon on the map, and they wouldn't let me launch it from my quest list. The next day I jumped on a different character, and it said to activate the scotopic ruin at the slab. I did that and poof, there was the icon. Hmmm, so i got on the original character, turned the rune on and there was the icon. Turned it off and icon vanished. While the icon was missing it showed the mission was partially completed, it showed the first fragment checked off, but I couldn't get back in until I turned that scotopic rune on. Is it possible people having trouble have the same problem I did? The stupid rune being off?

I'm not sure how or why but I went through the entire quest line and got the SMG. Wierd thing, though, is that I never did whatever is being done on the moon during the constant event there. I tried to get the orb to use to kill hive there but it said something like "can't handle corruption." I did all of the other steps with the intent of going back but that part never happened. But, I finished the quest, got the gun, and am using it.