I have had this same problem. The Axim was taking 1 - 2 minutes to resolve a different domain while browsing. Once on a site it would browse through it at speed. e.g Once on Google, it was fine. Change to BBC and wait 2 minutes. Browse through BBC and fine.
Spent a week talking to Dell support. Updated the ROM etc but to no avail. They then decided to send me a new machine with the updated network card etc and this was exactly the same.
So, I tried the Axim at a couple of Public Wi Fi zones and it was perfect. Also gave it to a colleague to try at home and it was fine. I can only imagine that it is some sort of incompatibility with my home D-Link wireless set up. I have Laptops and PC's throughout the house that work perfectly however the Axim just doesn't want to play nicely.
If anyone has any ideas, I'd love to hear them.