It has to do w/ your mmr. If your mmr is WAY below gold 5 (I think it has to be like down to silver 5, but maybe it's just a division so like being considered a silver 2 player by the game and losing would risk your gold 5 being taken) then you can drop but otherwise no.
You have 2 options basically. Either don't play ranked until after nov 11 so you get your rewards, or use lolking or lolnexus or something to look up the ranks of people you're playing w/ and try to stay at least w/ the large majority of people in your game at a minimum of silver I level. If everyone in your game is silver 2 promos or better I'm pretty sure you can't drop even w/ a losing streak bc you MMR is high enough still but I'm not sure where the cut off is that the game considers you so much worse than gold V that it will drop you out of gold if you're losing.
The only real reason to stick w/ the second option is if you want to see if you can get your games to be mostly gold V and gold IV players and actually hold your own in low gold, or if you're actually closer to silver ELO w/ a really good win streak that bumped you from silver I to gold V before your MMR dropped back to silver.