Re-do paint over plaster in bathroom: How to feather/match?
Here's how you get paint to stick to things. 

Scuff-sand.

Paint cannot bond to a shiny surface; don't take my word on it, try to paint a mirror and see what happens.  

Paint wants to see a surface that looks like Swiss Alps on a microscopic level - lots of jaggies and crevasses for paint to flow into and bond in shear.  To human eyes, that doesn't look like anything more than a loss of gloss.

But this requires a "scuff-sand"; my favorite tool for that is a green Scotch-Brite pad.  If you've ever gone to town with that on pots and pans, you know you can easily lift the shine off the pot.

So we're not trying to sand to level a surface; just to give it a microscopic roughness. Try around edges not to "blow through" an existing coating layer; that's not the goal. 

Without the scuff-sand, you are painting a mirror, and the new coat will bond poorly. *This is particularly a problem where gloss paint is used, e.g. bathrooms.  Satin/flat paint typically forms a roughened surface (to achieve the satin look) and that it easier to bond to (but I'd still scuff-sand it). 

Everyone is looking for "scuff sand in a can".  I am aware of many products which make that claim, but none I believe.  We certainly don't want any residue that could become the second threat: 

Remove contaminants.

That requires a washdown; typically with whatever removes contaminants, e.g. soap and water.  I also like to do one last 2-cloth wipedown with the actual solvent of the paint (e.g. water for latex), the 2-cloth makes sure you are lifting the contaminants away, not just smearing it around.  

Contaminants prevent the paint from bonding by sitting as a film between old and new paint.  Adding a layer that has no bonding strength to either the old substrate or the new paint.  So it's gotta be gone.

Sometimes the substrate is a contaminant, like trying to paint a 2-part LPU over, well, almost anything :)  In that case you need to use an appropriate primer as a barrier coat; the primer has different chemistry and is able to bond to both the substrate and the topcoat.  There are many other reasons to use primer, but that is one of them. 

Anyway, your predecessor did none of the above.  Typical. 

Any 2 layers that aren't bonding well will fail your entire paint job.

I have a machine where the original primer is separating from the substrate (because it was primed over mill scale).  Separately, the original topcoat is separating from the second painting's primer (poor prep in an oily shop).  Of course, it's not failing all at the same time, but in blotches.  There is simply no saving this.  No paint job can expect to perform well on top of a substrate that is failing. 

Again, everyone is looking for a product in a can that will magically fix this, and they're not looking for paint stripper :)  Unfortunately that's the only one. 

The answer for good long-term performance is "it's all gotta go".  This is the problem with letting monkeys paint your house, or applying products of poor provenance. You pay dearly for the mistake. 

Fortunately, latex paints are easily removed with comparatively mild paint strippers, so you're not having to go crazy with Aircraft Remover as you must with alkyds or LPUs.