It either your connection or theirs, so use a connection you know is really fast and reliable, perhaps at another office or a friends house.
Maybe the problem is intermitant, so you may wish to write a script that loads a periodicaly page and times the transaction. If you want I think I have something I could adapt to do that kicking about, provided you think you have a computer you can leave it running on for a couple days.
Alternativly try a server monitering service. A quick google turns up the following:
http://www.internetseer.com/home/index.xtp
If the problems occur when accessing from another network, there is a good chance its their end.