windows xp, being as old as it is, has limitations on many things, like how much ram the OS will see, how many records can fit on a spreadsheet, etc. it wouldn't surprise me at all if xp had a limitation on how many distinct computers can access a shared folder.
XP workstations weren't meant to be file servers. the network card may not have the bandwidth to support that many users. it could be a lot of things. but the bottom line is it doesn't work. I would recommend setting up a server (with actual server OS) for the purpose of file sharing. you can get a cheap NAS server in place of that too. if that's not in your budget, test the theory by perhaps setting up the share from a windows 7 or 8 pc. 35 pcs to one XP share sounds like pure OS limitations, and you may not be able to circumvent that by using windows 7. that many users accessing a single file repository is truly what servers are for.