Yesterday I visited Stack Overflow and had 13 consecutive days visited. Today, I visited and had 1. Is this a bug? Why did it reset?
A bug about inconsistent consecutive days has been reported. This doesn't quite fit the profile of what you are seeing. Hard to say.
Another possibility: It is easy to visit Stack Overflow every day and still "miss a day." Stack Overflow's days starts at midnight (UTC, over in London somewhere <grin>). So a "Stack Overflow day" starts at (for example) 8pm Eastern Time. So it is conceivable that you can simply log in one morning and, if you don't check back until much later the next day... technically, you miss a day-as-tracked-by Stack Overflow.
Also just opening the home page might not count as a "visit".
There was a bug reported a while ago about Safari's "thumbnails" triggering a "visit" (here) so you could actually achieve the Enthusiast and Fanatic badge without really visiting the site.
To get counted as a visit you might have to reload the home page or visit another page (just guessing here) and if you didn't do that it would reset your consecutive days counter.
While there were a couple of bugs in these site visit counters, your user history shows that you missed visiting on June 29th - please note that our servers operate on UTC time.