Hello Tim,
Thank you for reaching out and I am happy to help you.
When you saying WP-Cache, are you referring to W3 Total Cache Page Caching, or setting define(‘WP_CACHE’, true);
which is required for caching?
The most likely issue is that the pages are being cached once visited and therefore do not request the password.
I am not sure what you are using for the protected posts, but you should make sure to disable caching for logged-in users, and possibly exclude those posts from being cached by adding the to Performance>Page Cache>Advanced>”Never Cache following pages”.
I hope this helps!
Thanks!