This is a quite serious bug, rendering all meta SE's useless (in setups similar to mine). I noticed this problem a few days ago and it's still here.
I tested this on meta.bitcoin.SE and meta.math.SE using the latest stable Chrome on Mac.
When doing to the meta page using https, you get following warning:
When proceeding to the https-version, it's possible to login, but not to post questions. For some reason I get a CAPTCHA that fails to load.
When proceeding to the http-version. I log in and the page after the login page shows that I'm logged in, but clicking any link will make me no longer logged in.
If you read this question, it means that it is possible to use the meta.SO, so probably the problem is with meta.XX.SE being a sub-subdomain.