Essentially I've always wondered why any menu that can be expanded/collapsed never has it's state saved after you log out. I usually have most of my repuation/trade skill/skill trees collapsed so I'd only see the title, and not the huge amount of information under it.
Does anyone know of a mod that would do this? Is it actually possible?
The reason the trees reset when you log is that the default UI doesn't bother saving their state in variables, and just re-initializes them. It wouldn't be hard to save their state, but it's such a small inconvenience that I don't know if any AddOn authors have bothered to do it yet.
The 1.10 changes in the reputation tab are a nice start though - it now lets you specify factions as 'inactive,' and all the inactive ones are moved to the bottom of the list.