HTTPS / SSL randomly drops out

My Macbook Air (Early 2015) running 10.11.3 randomly experiences loss of access to HTTPS websites in all browsers, as well at the same time, iCloud and Mail app loses connection, and Skype also loses connection. I can still surf HTTP websites and ping any HTTP site. If I connect to VPN, I can access HTTPS, iCloud / Mail and Skype come back online. The only fix I have found (besides using VPN) is to restart the Macbook Air. Once I restart, everything is normal again for the rest of the day (usually). On rare occasions the problem happens twice a day. I'll usually just be surfing the web like normal and all of a sudden all secure connections die. Restart the machine again and everything is fine for a while.

I have a Mac Mini, running OS X 10.6.8, and an iPod running iOS 9.3, both running on the same network, and they have no problem accessing HTTPS. I have also switched to a different wi-fi network to make sure there is not something going on with my router, but the problem still exists on the new wi-fi network. So, it looks like it is isolated to my Macbook Air.

This has been going on shortly after I purchased this Macbook Air and upgraded to 10.10.3. It didn't do this with the stock OS X 10.10.2. The problem has been following since upgrading all the way to 10.11.3 (Combo Update). I keep praying that the next OS update will fix it, but it never does.

I heard there could be a problem with Keychain, but I've looked around there a bit without finding anything wrong that I can see. I did a reset of the default Keychain earlier today, but I just experienced another secure drop out a few minutes ago. God, I'm so sick of having to restart this freaking machine. I'm also sick of knowing that it is just a short matter of time before it drops out again for no reason.