Win2k Pro to NT 4.0-Red X’ing Maps

We have a Win2K Pro on our Net tied to NT 4.0 Server via tcp/ip with static ip’s. We can find and map the pro to the nt but as soon as we go back to my computer in a minute or 2, the mapped drives are red x’d.
Our application shortcuts to apps on the mapped drive open right up and a double clik on the x’d map also opens up. What are we missing? Thank-you!