Does Blender downgrade textures? Kinda focusing on what is not working here, but hey, I noticed that Blender kind of downgrades my textures/paint-work ... it gets a bit pixelly after I switch to Object mode and then back to texture paint mode..

Maybe its just my impression, but it does seem to me as if the textures get kind of bland and pixelly after a while....

I am using 2048x2048 px res right now, too small?

Am I alone in this? May I prevent this somehow?

Would be really nice if my textures stayed nice and smooth the way I paint them....
Blender doesn't change the textures in any way by itself and this applies to all possible actions. 

The texture size does not necessarily define its quality, it depends on the source (image texture, procedural material, tiling, up/donwscaling...) but normally I'd say that everything from 1k upwards is fine.

You might want to check Blender's System Settings. Hit Ctrl+Alt+U, go to "System" and play around with the settings for "Mipmap" and "Anisotropic Filtering". Deactivating them seems to help in many cases.