As someone who works in a support role (not for Zen or any other ISP) I can tell you that if staff are short the order is usually given by the department Manager to concentrate on the phones and pick up e-mail when possible because in the situation customers may have been on hold a while and will be none too happy.
However we are also told to stay with each customer until we fix the problem or collect enough info to be able to escalate the issue to someone to fix it (such as in the case of a piece of software conflicting with a certain brand of AV).
In Zen's case that might be fixing a server issue or escalating a fault to BT.
How long were you waiting for a response before you decided to desist each time?
Virgin (ADSL) => Namesco => Newnet => O2 => Plusnet => Zen => Newnet => Zen => Freeola
Note: I don't lay turf for anyone. astro or otherwise, all views and opinions expressed are my own based on experience.