Naturally Stealthy : You can attempt to hide even when you are obscured only by a creature that is at least one size larger than you.
Hiding (Pg 60):When you try to hide, make a Dexterity (Stealth) check. Until you are discovered or you stop hiding, that check’s total is contested by the Wisdom (Perception) check of any creature that actively searches for signs of your presence.. You can’t hide from a creature that can see you, and if you make noise (such as shouting a warning or knocking over a vase), you give away your position (ie you are discovered). Emphasis is mine
To me this reads as, when your position is discovered it's a done deal. You took your one hiding, gave up your position and now you gotta go find a new one rather than the one you just used. Now the comeback is going to be "well you are obscured and the obscured rules read... A given area might be lightly or heavily obscured. In a lightly obscured area, such as dim light, patchy fog, or moderate foliage, creatures have disadvantage on Wisdom (Perception) checks that rely on sight. A heavily obscured area—such as darkness, opaque fog, or dense foliage—blocks vision entirely. A creature in a heavily obscured area effectively suffers from the blinded condition (see the appendix)."
So in a sense I would treat the larger character like a patch of fog or something equally relevant. So in this case let's relate this to the fog idea, the idea that your character is in light fog. Yes you are obscured so you get your advantage shot and that's great. BUT after you take the shot you have revealed your place within the fog. The fact that you are obscured doesn't matter anymore because in my opinion when you reveal your position that's it, now that being said you could just move to another obscured square and hide right? I mean if we are in a big room of fog you see an arrow shoot out at you then you just move somewhere else in the fog and hide again. GREAT. So apply that reasoning but instead of the room filled with fog, it's just that one area behind the character which acts as the fog did. So when you shoot you get your advantage but again you have given your position away. Now you have to go to another obscured area and try to hide there, you can't use the same area. It make absolutely no sense to even entertain the idea.
Now that being said, if you had a line of fighters and you were the rogue darting back and forth behind this line, then sure I'd allow you to make hide checks and do you advantage, the key here is you have to keep moving into obscured areas that is different from your area you fired from during your turn. Also to move to another obscured area you would have to move THROUGH an obscured area because if you pop out from behind the fighter, then run over to a bunch of barrels you have given your position away at the barrels so I'd rule no advantage there either.