Miscellaneous quests disappearing from quest log?

If you visit Riften for the first time, right there at the entrance, a guy on the left side will stop you and talk to you. You then show him your gem, ask what its worth, and by this conversation, the quest (take the gem to an appraiser) will be removed and a follow-up quest starts, in which you must join the Thieves Guild, so you get access to Vex, which is the "appraiser" you were looking for.

If you have visited Riften, and have been talked to by that guy at the city's entrance, then your quest did not just vanish, but "upgrade" itself to the next level. Check if you have the MISC quest "Join the Thieves Guild". If you have it, all is good. Join the guild and talk to Vex. If you do not have the Thieves Guild quest, my knowledge is at an end.

Hope that helped, FRU33