I have (always had) the preference "Reopen last open files at startup" checked. However, it often does not work. In particular, when I log into my account and Skim is started automatically, because I had it running when I logged out, then it will not reopen the last open files. By the way, that was also the case under Mavericks.
The equivalent preference for my browsers and other applications (like TexShop and OmniGraffle) does work reliably. This even works, if your login session crashed.
By the way, it is also annoying that you lose your previous session when opening a single file directly from the Finder. An application like OmniGraffle will in that case simply also open the previously opened file, and I am quite happy with that.
You could always use the Restore Previous Session bookmark.
I really don't see what we could do to change this behavior, I cannot see how we can make the preference compatible with the system restore function.
How is that programs like Preview, TeXShop, and OmniGraffle do know how to do the right thing? They behave as expected; that is, when such a program is running with some open documents, then when you log out, and then log in again, that program will start again, and it will open all documents it had open when you logged out. This does not happen with Skim. Skim does start up, but without opening documents from the previous session.
Of course, if there is a menu item that will restore your last session, then it is not a big deal (I had not noticed this Skim feature; so, thanks for pointing it out).
Apple's relatively new window restoration mechanism is not compatible with a lot of aspects of Skim, including having the preference of restoring last open files (rather than either having it always or never).