Resolve then Not Resolve Host name

Hi Guys

I've been having this problem for a while now. What would happen is, Remote Desktop Would connect perfectly Fine to the other office One day then the very next day it wont be able to connect to the host but only to the IP Instead and this is a problem, because some of my co-workers have special permissions when connecting with the host name and not with the ip address.

The Fact is that there is a constant up and down thing about this problem and i would like to fix this thing once and for all.

Thanks guys, Hope you guys can help me out

Jono