Most often, the problem is always a result of high traffic through the door mixed with poor paint selection like using acrylic based paints rather than enamel based paints. In some instances it is also due to moisture sitting on the surfaces and moisture seeping in under the paint that eventually starts to lift the paint. It is also common for weathering to be found and to occur around the bottom of window sills as illustrated in the picture below.
One of the reasons this occurs is because condensation often collects and ends up sitting on the face or top of the window sill. The moisture will travel and sit beneath aluminum tracks and begin the process of rot and eventually it starts to lift the paint. Another reason is that the exterior timber quad lining the bottom of the glass on the outside begins to weather, shrink and rot and if exposed to the elements, then moisture and rain will find its way behind the quad and through the silicone into the inside of the window sill.
Preparation usually involves removing the existing paint by either scrapping, paint stripper or a light sand. If acrylic paints have been used, generally scrapping the remaining paint will come off quite easily. Fill any nail holes or exposed timber knots with a quality hard wearing filler. Give a light sand to the surface and remove/ wipe down any dust remaining ready for painting. Using a good quality oil based (enamel) paint, apply to the effected areas and allow for one day drying time. Once cured it is recommended to apply two top coats of oil based paint to the surface. Using an oil based paint will give you a harder wearing surface, whereas an acrylic paint is a lot more softer and prone to chipping . The end result will look like the picture below.
If you are undecided or not comfortable about painting the door sill especially for the front and laundry doors, then maybe you could consider applying 2-3 coats of an exterior marine grade clear varnish. This will highlight the natural timber qualities of your particular door sills and can be maintained quite easily with a coat of varnish regularly, without the hassle of preparation that painting requires. Exterior varnishes are better applied when door sills are new, but can be applied if existing door sills are painted. A little elbow grease is required with having to remove the existing paint, usually with a paint stripper.