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.
Solving Master Browser error
UNRAID server in Windows AD keeps setting itself as master browser
Computer Browse issue Domain - Software & Applications - Spiceworks Community
Computer Browser service missing on Server 2019
I wouldn’t mess with the router. You should be able to disable the Computer Browser service without any negative consequences. The service enables each PC to serve up a browse list for NetBIOS name lookups on the local network segment. If you disable it, the machine(s) simply won’t be able to serve up a browse list when other computers broadcast a NetBIOS name lookup request. For more info, check my post here: http://community.spiceworks.com/topic/274268-is-netbios-still-needed
Also be sure that the Computer Browser is enabled and set to Automatic on your DC(s). I think it’s disabled by default for server 2008 and up. If it’s enabled, the DC should win a browser election every time.
I have a windows network with 2 2008 R2 DCs at main site. I have a small remote office that has 1 XP computer always on the network and 1 XP computer that is sometimes connected to the network. The users at remote site connect to main network through VPN. There is no server at all in the remote office. Users do need to access information on the main network segment. I am getting the error “master browser has received a server announcement from computer Remote1 that it believes it is the master browser” and an election is held. I have been researching what to do about it. KB documents say to turn off the browser service on the romote1 computer or setup the router to not forward UDP packets. It would seem to me that turning off the browser server in the remote computer would be the better option, but are there any unintended consequences likely to result? If I were to stop UDP packets, what consequences would result there? I find it hard to believe that the browser service is the only thing that uses UDP. What is the best solution?