From here:
When SQL Server clients request SQL Server resources, the client network library sends a UDP message to the server using port 1434. SQL Server Browser responds with the TCP/IP port or named pipe of the requested instance.
Apparently when UDL or SSMS used for connecting remotely to SQL Server instance name, the query for resolving the instance name's port number store's somewhere in client machine.
I tested this by two client machines. When the 1434 UDP port was open first machine could connect to SQL Server instance name. Then I closed the port and tried again with that machine. The first client still could connect without the port being open. Then I tried with second machine but it couldn't connect.
I just wondering how and where this caching takes place?