More information/confusion:
An iPad connecting via a WIFI-to-3G router only works when the IMAP server addresses are given as 192.168.0.100.
The same iPad connecting through a normal ADSL WIFI router only works when the addresses are
www.xxx.com.au (which translates via DNS to the static external IP of the router).
This suggests to me that there is a DNS component to the problem.
In both cases, the iPad is getting it's IP and DNS server via DHCP from the router.
Any ideas?
Cheers and thanks,
Stephen