This behavior happens for me specifically for files/folders that are stored in my Dropbox folder.
I suspect it's due the the large number of code repositories with .git directories in my Dropbox causing Dropbox to register an insane amount of FSEvent watches, thus blocking Sublime Text from registering watches.
This would explain why, as Kurtis R.G. mentioned 2 years ago, other file watch using software like Grunt had problems, and why his updating, and thus restarting, Dropbox temporarily fixed the problem).
Here are the file and directory counts for my Dropbox folder. I'm going to try to trim down and see if that helps.
% find ~/Dropbox -type f -print | wc -l
% find ~/Dropbox -type d -print | wc -l
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