Can’t select blog month within archive category

A canonical redirect:

The GET parameter m can trigger a canonical redirect when permalinks are used.

The canonical redirects are activated with the following hook:

add_action('template_redirect', 'redirect_canonical');

where redirect_canonical() is a rather complicated function.

Here’s the skeleton of the part that’s active within this “monster” callback:

// ... cut ...

if ( is_404() ) {

    // ... cut ...

} elseif ( is_object($wp_rewrite) && $wp_rewrite->using_permalinks() ) {

   if( ... ) {

      // ... cut ...

    } elseif ( !empty($_GET['m']) && ( is_year() || is_month() || is_day() ) ) {

        // --> We are here <---  ;-)

    } elseif( ... ) {

    // ... cut ...

}

// ... cut ...

where $_GET['m'] is non-empty.

In your case when $m has the YYYYMM format, is_month() is also true and we get the following redirect:

$redirect_url = get_month_link( substr($m, 0, 4), substr($m, 4, 2) );

so we should be redirected from:

http://example.tld/category/category-1/?m=201503

to:

 http://example.tld/2015/03

A possible workaround would by to use instead:

http://example.tld/2015/03/?cat=16

to avoid the canonical redirect process.

You should also try this on a vanilla install: default theme and no plugins to avoid your infinite redirect loop problem.