I used to experience the similar issue. In my case the preload never cached all the pages. For some reasons the preload process could freeze on any moment. But all the rest worked well, so it made cache page when you open it directly via a browser. So I decided to “open” all the pages “manually” on a regular basis.
Of course I do not want to do it by myself so I use cron schedule on my web server and a wget program.
– I switched of the Preload completelly (“WP Super Cache Settings” -> “Preload@ -> “Refresh preloaded cache files every” ->0)
– prepared bash file “mysite_cache.sh” that executes the following code
rm -rf /tmp/mysite_cache_update
wget -r -l0 -o /tmp/log_cache_update -P /tmp/mysite_cache_update -X /wp-content,/wp-json,/wp-includes,/feed http://mysite.com/
– and configured cron schedule that executes the bash once a day after midnight.
I beleive you can use the same approach and do the preload “manyally” whenever you want.