Since my last post, the season (number 4) ended, and I finished Silver 4. Provisionals in Season 5 dumped me back into Bronze 3. After many months of fighting, and a few lessons, I finally made it back into Silver.
You can see something changed in September. I went 13/15 with Caitlyn on a stretch in there. My Challenger coach said "One of you main jobs is not to die. If you're dead, you're not getting gold, you're not getting XP, and you're not dealing damage. I'd rather you're 0/0/10 than 6/5/6." It sounds stupid, but this was a really important piece of advice. It took a while for it to sink in, but I started playing not to die.
Suddenly, my week stats looked like this:
Many more kills than deaths, which is really what you want on an ADC.
Another thing he (or maybe it was my other platinum coach) told me was this: "Every time you back (until the first bot turret is down) buy two health pots and a ward." This has also made a big difference. I had not been buying wards or pots (after the first one) because I thought of them as gold lost due to being consumable. But it's much harder for their jungler to gank you if you've always got a ward up in the river and tribush, so in the long run, you don't die as much.
To see what "playing not to die" looks like in practice, you can watch this game where I was against a really aggressive Jinx.