So all traffic is increasing? Not just changing from direct to now being reported differently?
Here's one option:
do you have separate mobile URLs? We saw the same patterns and here's what happens:
iOS updated back in late July (mentioned above as August, but it was actually like July 30, so close enough). So referrers were now passing - no search term data, etc. but at least you were getting the referrer as opposed to just looking like direct traffic before.
However, if you have separate mobile URLs and Google mobile is indexing your non-mobile URLs, then when you do the user agent detection and redirect to the mobile URL, you are basically redirecting the referrer off before and it doesn't get captured in your analytics.
But, Google is now starting to make changes to show the mobile versions directly in the search - when they changed ours it was the whole site all at once showing mobile URLs instead of the standard ones. I know we're not supposed to give examples, but it's a health information site - i'm sure you can find examples for queries in that space in mobile if you wanted.
I would look for your site in Google mobile SERPS and if they are indexing your mobile URLs now, then it's probably that change that made the data look different, but really as a result of the July 30 change to allow referrals in the first place.
If this isn't it and you don't have separate mobile URLs, then you might want to look at any configuration change on your end for mobile traffic that might have an effect on how the passing referrer might be handled.