Hi @SherylM,
Welcome to the Bunnings Workshop community, it is fantastic to have you with us.
If you had some photos of the wall that you could upload, this would certainly help to either confirm my suspicions or help identify the cause of the issue. Let me know if you need a hand uploading images.
This usually happens when paint is applied directly over bare plaster without the use of a primer, which seems like a likely reason for the issue. Primer binds the powdery surface and creates a surface that paint can cling to. Without the primer, the paint struggles to bind to the surface.
If it is a lack of primer, as I suspect, you will want to remove the existing paint from the wall using something like this 100mm Sharp Edge Paint Scraper or this UNi-PRO 100mm Heavy Duty Wall Stripper.
Once the old paint has been removed, you'll want to brush down the wall to remove as much plaster powder as possible, then apply a primer such as this Dulux 1Step Prep Primer, Sealer & Undercoat, followed by two coats of your wall paint.
Check out How To Prepare A Wall For Painting and How To Paint A Room for some further guidance.
Let me know what you think and if you have further questions, please don't hesitate to ask.
Jacob
