So, I finally encountered the strange bug which I saw mention of some time ago.
For the June 6 daily, I tried to play it quite close to the expiry time, and after picking preps and pressing play, the game just froze and did nothing.
After figuring out that I couldn't do anything, I had to close and relaunch the game.
To my horror, found out that the game claims that I have played my daily, which I have not.
Also tried closing and relaunching Steam and the game, and got the same thing.
The day rolled over and there's a new daily. Amazingly, my streak is not broken.
And my total wins didn't increase either and if you check the records for June 6, my results are in limbo.
Now, I don't know whether attempting the new daily will continue my streak or reset it to 1 (will try it later). But surely this is one weird bug.