Browser's session times out after 20 seconds of inactivity (right nuisance!) - solved
 

So, I'm getting thrown out to authorisation window every other minute when working with e-mail via web-interface.
After clicking on "Times and Fares" at nationalexpress.co.uk here is what I get:
http://www.virgo123.greenline.ru/hp.cfm
Here is my cookies settings:
http://www.virgo123.greenline.ru/prefs.png
echo $TMOUT displays "0" (if relevant).
I'm using Firefox 1.5.0.8 / Mandriva 2007 (2.6.17-5mdv)
On Windows XP with Firefox 2.0.0.1 there is no problem.

IMHO session timeouts usually indicate problems with reading cookies which in turn points to Javascript scrubbers like FF's Noscript plugin, browser Javascript settings, cookie settings or, where applicable, scrubbing proxies. Enough leads for you to check out, I hope.

The usual "block cookies" option in firefox may also have that effect on web sites that automatically reload the page.

Solved.
After I updated Firefox from 1.5.0.8 to 1.5.0.9 problems disappeared in both cases - with email and ticket bookings.