And this is why I don't want to do a hard reset. I have "Hey Cortana" and she's working just fine. I use it daily and don't want to have to revert back and re-enable it. I have no big issues with build 14393.82 at this time!
I have the same issue. Haven't tried any troubleshooting steps yet, but I don't really use Hey Cortana much so it's not a huge problem for me. I did a hard reset immediately following the update from 10586.545 to 14393.67, so I wasn't sure whether it happened after the update or after the reset.
I downgraded my Lumia 930 back to Windows 8.1 to get Cortana & Hey Cortana working again. Battery life has improved back on 8.1 as well compared to Windows 10.