I'm susposing that these 2 machines are in the same domainand not in different ones.
Now since you've already told us that you are using both 2K and NT4 I'm assumoing that the 2K installations are in "Mixed Mode" so they can see and comunicate with the rest of the network.
Without further information I'd start looking at the server at the head of this domain or what is more likely the computers themselves which are giving problems. Has anyone recently added some new software or upgraded hardware drivers? What is the configeration of these indivual computers as the hardware may be incompatable with other parts of the network here I'm thinking about the 2K installations and the Service Packs that are involved in keeping them up to date.
Obviously there is a problem with their communication with the server that they are attempting to write to and then some basic flaw in the unit that continuallly losses its printer driver.
I had a similar sought of a problem recently with a computer that had been in service for a few years running 98 SE and it would only pickup the network card once in 20 attempts. It didn't matter just how many different network cards you put in the thing it just would not accept them event hough it at first reconised a new component and asked for the proper install disks but on reboot there just was not a network card present in the system most of the time. The only way I found to fix this problem was to replace the unit with a different one and I ended up putting it down to a badly made M'Board and the cheap unit that it was.
If you can give some more info on the setup I'll attempt to think about you're problem and come back with some sought of answer but if they are of the cheap nasty varity M'Boards/computers the only true fix may be to replace them with something newer from a different section who currently needs upgraded equipment.