Consistently Slow performance with Server Publishing site feature enabled

Back from holiday to find the SharePoint 2010 site performing slowly.  On the previous day, there was an issue with SQL Server Agent and this needed to be restarted, but this may be unrelated.

The problem I faced was that seemingly every site or page was being delivered as expected, only with an additional delay of 10-15 seconds each time, consistently.  After this 10-15 seconds, the page would load instantly.  There was no mention of any problem in the system or SharePoint logs, and the latter was showing the usual request completion times.  It just seemed like the request was being held for 10-15 seconds.

Two site collections were unaffected: MySites (which is out-of-the-box SharePoint 2010 stuff) and Central Administration.  These both operated as usual, with response times between 1-2 seconds.

I later discovered that sites that have not had the SharePoint Server Publishing site feature were not affected.  To confirm this, I created a new Blank Site, and the pages loaded instantly.  As soon as I enabled the SharePoint Server Publishing feature, the performance problems reoccured.  Deactivating the feature did not fix the problem, so it seemed that any site that ever had this feature activated was afflicted.

Following this line of investigation, I checked the existing sites that had SharePoint Server Publishing activated previously. This feature was now deactivated on all sites, including the root site.

Following guidance from our SharePoint support contractors, I tried to view the Site Collection Output Cache settings.  This gave me an error, saying that the list does not exist, and a quick Google suggested I deactivate and reactivate SharePoint Publishing Infrastructure site collection feature.

I left this for the day, planning to try this when I came in this morning.  But when I signed in, the site was operating perfectly again.  The Server Publishing site feature was, again, activated for all sites.  I've looked through the logs to see if anything changed overnight, but can't see any record of this.  No-one in the office, or any of our contractors, made any changes to the server farm.  So, this is unsolved.  We do need to find out why this happened so we know how to prevent or fix it in the future, but so far, no solution.