Not only it "forgets" open files, but also project folders are not restored. I expect it to keep folders in a project.
So when remember_open_files is set to false, Sublime starts with a completely empty project: no files, no folders. A bug i guess?
Also, one related suggestion:
Consider a big project with several folders and many open files. Every time i open some unrelated text file from Windows Explorer, Sublime opens, loads the whole project, and the file gets lost among others. Remember_open_files cannot help in this case.
The solution: sublime should not load last open files/projects when it is used to open a file (i.e. check on launch if argument count > 0, then do not load previous session)