Win7 desktop can't access network share while updating Group Policy causing GP to fail

I've got a bunch of desktops that are members of a domain. There's a couple of group policy items set on these, and some of these involve copying files from a network share locally (things like config files etc.)

All of my desktops work perfectly, except for one, which was recently rebuilt. For some reason, this loses the ability to be able to access the network share while it is updating its Computer group policy. I noticed this because all of the GP-managed config files were missing from the desktop, and a bunch of entries existed in the EventLog similar to:

The computer 'example-config.cfg' preference item in the 'Default Domain Policy {31B2F340-016D-11D2-945F-00C04FB984F9}' Group Policy object did not apply because it failed with error code '0x80070040 The specified network name is no longer available.' This error was suppressed.

The network share is accessed through an IP address, rather than a DNS name (I know, I know), so I don't think this is a DNS issue.

The strange part of this is if I RDP to the desktop, I can navigate to the network share containing the config files just fine. However, if I open a cmd prompt and hit gpupdate /force, I'm suddenly not able to access the network share. It basically times out. The gpupdate process then runs for far longer than usual, and once it's complete I can access the network share again.

The only thing that's different about this desktop is that the hardware is different (NIC, Gfx, motherboard etc.) How would I go about diagnosing what the problem is here?

The PC connects to the network shares for part of Group Policy using the computer's account. something like MACHINE$. Detach the box from the domain and reboot, rename it MACHINEA or something and reboot, then reattach it and boot again. Move the computer account to the right OU, wait 15 minutes, then boot again.

About 90% of the time that sorts out GP issues at the Computer level.