Nothing much to add here … I also started receiving 1016 and even wrote a ticked (no answer) but no development happened … UNTIL TODAY, when trying to test the stability of the connection, and receiving 1016 only once (from 4 attempts) … the other 3 - crash and return to desktop. Lucky me 
And before someone asks why I create a topic in the Technical Support section of the forum without asking for support on the problem - well why I ought to ask, if no support is given to anybody else that asked before me
I am having the same problems, every 5-10 minutes I keep receiving 1016 errors.
tried resetting router, ipconfig renew, flushdns… Checking if drivers are up to date. I don’t have issues with other games.
i’m getting it more and more now, if i’m doing bounties it lets me do 3 or 4 of one act and then the error pops up. The sooner blizzard admits that this is a problem at their end the sooner and look into it, the sooner this problem can get resolved. I like this game but error 1016 is making it unplayable. I’ve always wanted to do a HC character but won’t ever do that whilst Diablo is a online game only. Wolcen did a online only server and a offline only server, why can’t blizzard do the same?
Same here, sometimes I can play for 2 hours, sometimes it’s only 15 minutes. Always error 1016 and I’ve also done all the troubleshooting steps.
The odd thing I’ve noticed is that it always happens with no lag
Reading through some of the other threads on related issues re, error, game freeze, disconnection:
I disabled in-game sound, music. Switched back to bit 64 from the game options in-app.
Seems to have solved these issues (incl 1016) for the moment