I don't think it's the plug depth as I have tried it on a couple of cables with the same plug depth and some will work and some wont. Don't know why though. I do believe it is a cable issue though and not a adapter issue because I can get the same cable to work on two different adapter output amperage.
Trust me. It's the plug. Take one that doesn't work. After it's inserted, very slowly pull it out a bit. Notice the temporary connection.