Hello Marge,
Thank you for reaching out.
There are no reported compatibility issues so far with aMember Pro plugin and W3 Total Cache.
Since this plugin is managing logged in users, make sure that if you are using Page Caching that the option “Don’t cache pages for logged in users” is enabled, and disable the set expires header and cache-control header in Performance>Browser Cache>HTML&XML section of the plugin. Make sure to save all settings and purge the cache.
Thanks!