I was having precisely the same issue. During the fifth unsuccessful attempt I FINALLY noticed that one of the dialog boxes was asking me to confirm that I really wanted to upload the file "C:\fakepath\DIR628A2_FW124NAB01.bin". What? fakepath? I made a new folder called fakepath in the root directory, copied the .bin there, and tried again - everything worked like a charm! It does, however, revert the router back to all of its default settings, so either export those first or be prepared to redo all of your settings.
Must've been a bug in the 1.13 firmware...