After about 5 or 7 losses in a row at 0 LP in Silver you will likely be demoted.
I will say, after looking at your stats, you appear to be doing OK. Even if you were to get demoted from Silver to Bronze, you would likely advance right back into Silver.
Support is the hardest position to carry from in lower Elo. You will continue to struggle winning games despite playing "well" if your team makes frequent mistakes.
Support is my secondary role. I am serviceable as a support in my Elo, but I am a much better Top and maybe mid (not sure). Recently, I played as Leona in my promos. Got an S, probably played my best Leona game ever (I only recently started playing her in ranked), still lost though. I made two mistakes in two separate late game teamfights. Essentially, my team was incredibly fragile (as a comp) and I missed my ultimate in two separate teamfights on the enemy assassin.
But my team had a high amount of deaths. I also know, I put them in a position to win the game A LOT earlier. However, we were not grouping or taking objectives earlier, just skirmishing. Eventually, these mistakes allowed the opposing team to capitalize on two seperate late-game fights leading to an end game push.
The point of the story is that to be a support you typically have to play almost a mistake free game to win. At lower Elo, you probably have to play BETTER than B+ grade to win games to climb AND you also have to quickly recognize the skill of your team.
When your team plays poorly, your job is to try to band-aid the weaknesses, while also enhancing the strengths. This is tough. If your ADC is outmatched, it is very difficult supporting him/her in a losing lane. Then your task becomes supporting another player that isn't doing as poorly and hoping they can carry and let your adc catch-up on their own.
My biggest problem is I will sometimes miss a skillshot in a crucial fight. I also die a bit too much as a support, in Gold (still working on that).