The problem is that mod_pagespeed does not proactively freshen resources when the server is idle. It only does so in response to requests from clients.
There are several ways to compensate for this:
1. Run a cron-job to crawl your site with 'wget' every minute.
2. Use LoadFromFile if possible -- this often makes it possible to get instant responses once a resource is initially optimized.
3. Increase ModPagespeedRewriteDeadlinePerFlushMs to (say) 5000 (5 seconds), which would increase the latency seen by clients requesting the page for the first time since the resources expired, but would make it much more likely the optimizations would increase in time.
Any one of these could work.
-Josh