I had this same problem, and I think I have identified the source, at least for my setup. I am using Sublime Text 3 build 3059 portable 64-bit on Windows 8. I didn't have any problems until recently. Before I figured out what it was, I also tried turning off ST3 indexing, my anti-virus (avast), and Windows Defender, none of which fixed the problem.
Turns out, the problem was editing the text file in Boxcryptor (https://www.boxcryptor.com/) was a problem, probably because of the file locking. When I use ST3 with an unencrypted file outside of Boxcryptor, it works just fine. I'm using Boxcryptor with Dropbox, so I tried it with an unencrypted file inside of a syncing Dropbox folder, which also worked fine without any slowness.
Sadly, it looks like I can't edit files easily, so I am working with a local clone on my desktop, which I sync with the Boxcryptor directory. I don't know if there is any luck with other cloud encryption services, but I don't have time to try them out now. Hopefully, this helps out others who have a similar workflow.