hook_page_alter called once I have a Drupal 7 theme which is a Bootstrap child theme.

In my version of page.vars.php, I have a THEME_page_alter() call which runs only once until I do a clear cache. Other hooks such as THEME_process_page or THEME_preprocess_page are called each time I reload the page.

A second theme, with the same page_alter hook works just fine and is called each page-reload without the need for a clear-cache first.

What could be causing this?
Theme settings are specific to each theme. Go to /admin/appearance/settings/yourtheme and check for any theme-specific caching options. I can't tell you exactly what the options would be because that depends on your theme.