It's possible the paint still needs more time to cure and stick. It could also be a problem with the paint or the lack of priming (surface prep) before painting.
1- You didn't mention the sheen of the original wall paint or the brand and sheen of the new paint. If the original paint is a semi-gloss latex and the new a satin then it will take up to a month for a good cure to form and stick down the new paint. A slick surface slows down this process plus the new paint will have a hard time getting a good bond.
2- If the old paint was an oil base and the new is a latex then you will always have this problem. All shiny and slick surfaces need a good bonding primer prior to painting. It's also possible that your new paint is either low quality or defective.
At this point I recommend waiting 2 more weeks and see if the bond is improving. If not, the only way to fix this is to remove all loose paint, lightly sand (non-textured walls only) and prime before repainting.
Removing the new paint could be as easy as using hot water to loosen it and a scrub rag to help get it off the wall.
There isn't any quick easy fixes for this problem. Sorry.