I'll grant you this is an odd problem... and a possible answer gets off in the deep technical weeds pretty quickly...
You're question implies you have multiple DCs (Domain Controllers), so I am confident that you are familiar with their basic function--what follows is for other readers of this post: Domain Controllers are used to authenticate users and services on a network (they validate that you are who you say you are). They also often double as Active Directory integrated internal DNS Servers (machines that map names and services to IP Addresses and vice versa)
They also occasionally are used as DFS (Distributed File System) Root servers... I could go on...
Every function I just mentioned has some capacity to cause your problem in the right combination of circumstances.
For example, if you have 4 DCs, but only one is acting as a DNS server, when it goes down, you have reduced capacity to resolve the names of any network resources, such as the UNC Path to the template source \\SomeNode\Templates.
A DFS Root is a node that simplifies network sharing... if you're using it, and your DC is hosting the DFS Root... it can't redirect callers to the proper node.
One thing does seem clear... the word documents that are giving you fits are attempting to connect to some network resource, probably not the DC, and the DC is playing havoc on name resolution of the resource, authentication to touch the resource, or both.
Deeper still: Not all DCs are the same... when you get some free time Google "Single Mastered Operations"...
Best luck.
--Lilliabeth