I'm on US East Coast time, and I've been logging in every day, but because of, I assume, a timezone difference, my profile says I've only logged on 8 consecutive days. What timezone is Writing Beta actually on? And if this isn't a timezone thing, what is it?
Stack Exchange generally uses UTC for all timestamps. See also What is an SE “day”? When does each day start?
In a few cases, it uses the rule of "somewhere in the world". I believe that's the case for Winter Bash and April Fools, for example.
As noted in the comments, just logging in isn't necessarily enough for the day to count as having activity. However, browsing and actively using the site while logged in should. The details are vague here. If you care a lot, check your profile's "last seen" field; that should be authoritative.