by Kale » Sun Jan 31, 2016 6:54 am
The gossip skill is one of various rewards you get from the Thieves Guild in chapter 3. The guild is a bit peculiar, since all the rewards you can earn are reset after each quest you complete for the guild. This means it is very easy to complete two quests back to back, and lose one set of rewards, including the gossip skill. If you do have the gossip skill, it is in Random's spell list.
Apart from (I believe) needing it for one particular quest, the utility of the skill falls off immediately and it is basically never used again as far as I can recall. The perception, mercantile, and persuasion points you can earn from the guild are far more valuable in the long run, so hopefully you got those.