I thought I'd better post an update to this since it is all working great now, and since it doesn't appear to be mod_pagespeed's fault there could be tips for anyone else experiencing it.
I can't definitively say what nailed it - you can see from what I wrote it was intermittent but fairly frequent. Since these changes, there hasn't even been a hiccup :-)
1. We were running Ubuntu 14 LTS and upgraded to Ubuntu 15 LTS
2. We had a version of the mod_pagespeed conf file which hadn't changed for years so brought that up to the current version (not many changes needed actually)
3. We *think* the ulimit on open system files was 1024. It's now much bigger.
4. There was a MySql max open file limit of 4096, this is now much higher.
If these file limits were the culprit we'd have hoped to have seen immediate problems manifest in other areas.
So we like Mondays again!