After visiting "tags" page, my permalink structure seems to broke...

I have installed, the plugin, and noticed it created succesfully the "tags" page. So first noticed the page says "There are no tags to display" - but I guess this is because it is a fresh install of the plugin.

But the weird problem is that each time after I was visiting the /tags/ page, the permalinks to archives pages (including categories, tags, and dates) does not work - redirecting to wp 404 page. Only links to individual posts continued to work.

I had to go to Settings -> Permalinks and click save to enable it again. That happend each time after visiting /tags/ page - so I had to deactivate the plugin.

I have attached a screenshot of my Permalink settings. Also I use the Romanian transaltion of buddypress.