As most have already mentioned, those plugs and screws are just not man enough for the job.
I had the exact same problem with a plaster wall. Used even bigger plaster plugs for it. The wall was just too soft.
In the end I used some spring toggles which spring out as they are inserted through the wall
There are other fitting butterfly clips and toggles and plugs which will do the job
But those plugs u got there? No good.