Doing a bit more research, it looks like there's a limit to how many files a given application can have open.
The first thing I'd like you to try doing is opening up the Sync preferences on your mac, and pressing the "Show Clients" button. A sheet will slide out that shows a list of machines that are syncing with your database and when they last synced; if there are duplicate entries in the list, or entries for machines you don't sync from any more, please remove them from the list by selecting their entry and then pressing the "Unregister" button.
If you close the sheet and press the sync now button, does the sync still fail?
If so, please send an email to the support ninjas with a link to this forum thread and the output that you get when you post this command into a Terminal.app window and hit return:
we'll use that info to figure out what exactly is going on here.