Painting skirting board already painted with glossy paint
Painting over older existing paint, especially gloss finish, requires preparation.  The two things that most interfere are surface contaminants (such as grease, dust, other deposits) and lack of tooth (too smooth a surface).

On your new sections, cleaning the painted surface with soap and water or with a solvent cleaner (like mineral spirits) will generally solve the first problem. Light sanding (usually about 120 grit), followed by cleaning with mineral spirits or wiping with a tack rag will generally solve both. There is also a mild chemical stripper called a deglosser that roughens the surface somewhat like sandpaper.

Just painting over an older glossy paint will often lead to poor adhesion. The section already done is not easily fixed except by sanding and cleaning to remove any of the new paint that is still loose and to roughen up the exposed old paint. Then follow with a new coat of fresh paint.