Users can't write blog posts?
Using Jamroom
Yep, I would have asked that question. But is not that. The BLOG tab is showing on the screenshot, so its not the quotas, its just the button thats not showing, weird.
The other typical response: Have you ran the integrity check and cleared the caches?
With that out of the way, try switching skin to elastic and see if it persists. I have a dev server setup of your site here and am not seeing the same issue her. When logged in as cheshire-cat I can see the blog + button.
So my guess heads towards: Have you made any customizations to the blog template module files?
If the user goes to the YOUR-SITE.com/blog/create screen do they get error messages? If yes, then its something blocking them from creating a blog, if No then its just a missing button.