Pager missing on pages greater than 1, but returns on a refresh

We have a Search Index View that renders all nodes of a particular content type that match whatever keywords have been entered into the exposed`search_api_fulltext` filter. If nothing has been entered into the exposed filter (i.e., the default when the page is first accessed), then all results are shown.

The View uses a pre-configured view mode to display these nodes, and the exposed filter form is displayed in a separate block.

In addition, the View includes a "full" pager that has been set to display 20 items per page. Caching has been disabled entirely (i.e., "None"), and the View *does not* use AJAX.

What we're seeing is that when there are more than 20 nodes, the pager loads on the first page only. If we click to the next page--or any thereafter--the pager disappears. We can bring it back, however, if we do a simple page refresh... which makes me think it's a caching issue.

I checked the variables available using a template_preprocess_pager() function, and indeed the "items" array is missing when pages greater-than-one are first loaded... only to return if the page is refreshed.

We are also using facets, but even when I try removing the facet blocks entirely the pager is still missing on pages > 1.

I'm at a loss as to where/how the pager is called/rendered, and how to fix it. Any help would be greatly appreciated, and please let me know if there's any more detail that I can provide.