@liverpoolfcfan thank you very much for the detailed explaination.
This server is the busiest we have, there are ~90 users and 130 AS sessions (not all active). Most of them are with normal handeld devices, but there is a percentage of Outlook clients, which are the most problematic ones.
Anyway the server load is very low, always lower than 0.3 and rarely going higher. Using ZWC is fast, so I don’t understand why it’s sometimes slow on AS replies. The infrastructure is not really up to date: Zimbra 8.6, PHP 5.5, ZP 2.3.9, backend 67.
I’m going to migrate state files to MySQL to see if it helps in improving performance.