The issue: What I found was that only one Imperial City district's daily repeatable quest is available at a time. Dropping one of these quests allows you to pick up another or the same in any district. You can only have one district's quest at a time, however, even if you take the time to zone in/out from your alliance base's ladder network to try to pick them up or perhaps are returning with an old one still in your journal.
Opinion/thoughts: This seems like a pretty silly way to arbitrarily force players to slog back to base through the sewers between every turn-in of the only current long-term PvE content besides monsters/bosses and instanced dungeons in IC. The time wasted running back and staring at loading screens to turn these quests in could be better spent doing almost anything else in IC at a better payout of Tel Var Stones (assuming you didn't just accidentally complete it and/or were headed back to base anyhow). Unless perhaps the satchels have chances for certain rare drops, there is little incentive in picking these up, much less spending time focusing on completing their objectives. Now, if you could pick up all of them from your alliance's base and then cruise through the districts to the tune of 6 quests for a total of what I estimate to be around 480 stones for somewhere around an hour of questing with only one run back - that might be worth it and would only take shuffling the current quest givers. Throw in an extra hour or more of running through the districts to hit the sewer hatch closest to base and hoof it back between quests (as it is currently), and you're better off not bothering and mindlessly mobbing a boss or two in the sewers while saying, "Lulz whut quests?" instead.