Microsoft describes it as the following:

Determine if the master browser has the server's name in its list. The master browser is the first server in the chain of communication that must contain the missing server's name

Source: https://support.microsoft.com/en-us/kb/188305

Additionally:

The Master Browser is responsible for the browse list within its respective subnet and portion of the domain on its subnet. The Domain Master Browser is used to collect information from each of the Master Browsers via the NetServerEnum API call. Once collected the list is merged with the Domain Master Browsers list for its own subnet.

Wikipedia - Domain Master Browser

Yes, Domain Controllers should be Master Browsers - setting your domain controllers as "Preferred Master" (registration wall; try archive) should fix most of the Master Browser election problem.

reg add HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\Browser\Parameters /v IsDomainMaster /d True /t REG_SZ

One of the common reasons for operating a WINS server is to provide a central reference for NetBIOS names across several subnets. Choosing one primary WINS server and pointing all clients to it lets NetBIOS name resolution work across subnets without requiring the use of Domain Controllers.

But if your system is supposed to rely on domain controllers, loss of replication for site C may explain your symptoms. So start with verifying successful replication.