'Because your session timed out, we have reset the search page.' issued when visiting a search page

There's no warning when I visit other pages, but it starts as soon as I try a search (simple or advanced) the first time regardless to whether there was a previous "half-filled" form or not.
This happens only on Chrome, not in Firefox.
If I visit a different page, I get the warning only the first time and nothing until I try to do a search again.

Using Google Dev Tools I noticed the Network tab lists a number of requests (about 18) made to the URL /civicrm/contact/search/advanced?reset=1 all with method HEAD.
The URL of these requests is always to 'advanced' even when trying a simple search.
Chrome's console does give an error "Too many redirects"