In all honesty it sounds like you have other problems that are causing the samba server not to become the master-browser. Or in other words, not being the master-browser is another symptom. Not the cause. Being the master-browser does NOT have anything to do with being able to connect to a network share or not. It is simply a left-over technology from days-gone-by from old "NETBIOS" days. The master-browser is simply a machine who is currently most-likely the guy who knows the most about the local network. The only information that server has/provides is a name-association to an IP address for a specific type of service. The list is not typically crucial, as other methods of discovery are tried. When in doubt, you could always create a lmhosts file and hard-code values on one machine in the network to ensure the values are correct.
In most networks today, all this lookup-stuff is done with DNS. (...and in corporate networks before DNS they used WINS) NETBIOS stuff is rather messy and excessively chatty on networks.
Answer from TheCompWiz on serverfault.comForce SMB master browser
Samba domain | The FreeBSD Forums
Constant messages in log about Samba 'local master browser', despite Local Master option being off
[SOLVED] Which device should be the Samba (SMB) "Master Browser"? - General Support - Unraid
I don't actually NEED to know. I'm just curious. The fact that I can't seem to find a straightforward answer to this question via Google suggests that either I don't know how to use Google any more, OR that knowing which machine is master browser isn't really a thing and I shouldn't bother with it.