Still not sure if it's relevant but hope it could help someone.
I was struggling to fix my snippets auto-expand feature. Read all the threads on the topic, checked all the Safari plugins, Google Chrome issue, Accessibility re-enabling trick, quitting all the apps, checking non-standard apps like Karabiner-Elements (which I suspected first), rebooting my laptop dozens of times while trying to fix an issue, etc. Literally everything. Nothing helped. Still wasn't able to fix my snippets expansion.
So after trying everything I decided to load my system (macOS Sierra, 10.12 with Alfred 3.1.1 Build 736) in a ’Safe mode’ without any ’Login Items’ or whatsoever. There I loaded Alfred and everything was perfectly fine - snippets where auto-expanding. So I concluded that it must've been some kind of a conflict with apps I used in a normal mode. After loading all the apps possible I still wasn't able to break auto-expansion, therefore I decided that it was some kind of a system underhood stuff which wasn't breaking Alfred in a safe mode but obviously was when I loaded my system in a usual way. Well, desperate, I decided to load my system back and wait for a fix from Alfred authors in the future. Anyway, I wasn't able to write a propper bug-report with any adequate reproducing steps (cause it just didn't work, without any obvious steps to make it so).
Imaginge my surprise when after loading my system back I found out that Alfred snippets auto-expansion feature was perfectly fine. I tried to load anything unusual to reproduce the previous issue, but it seems nothing could break auto-expansion anymore. Still works for me, even though I'm not sure if it was a 'Safe mode' which fixed it. Anyway, if you tried everything and all the tips failed try and reload your system with a Shift button pressed. I bet it won't make any harm but could bring your snippets back! Good luck!