Oh, i do that on purpose and theres another workday--maybe two--that can be repeated. Misinterpreted your meaning being there's a Shenmue 2 exclusive glitch on February 2nd 1987. Tough enough with how slow I like to take Shenmue plus all the extra work days to cash in on toy capsules etc; barely able to do the Famgei bday sidequest since back in 2003/4 when 2x was still new.
I was also stuck on it for awhile, too. Didn't even notice a pattern or which route I took to pass to the next story day until a few play-throughs haha. Read somewhere the Japane version does not have this glitch? If so, I theorize the multiple days you can avoid advancing the plot, were introduced purposefully-on-accident. CONSPIRACY