Is it better to add a network segment to a growing network or continue to use the same subnet mask?

It really depends on the statistics that your growing network shows. Thus, if there no "down man" devices or unused addresses present in the network, it would better to add a network segment rather than overload the current network. 

Growing networks start to suffer from network congestion. When you segment the network, routers are better able to route traffic to specific parts of the network without broadcasting signals across only one segment. When you reduce broadcasting, you lower congestion, which speeds up your network. With a growing large network, it’s better to start segmenting the network and create subnet masks for different segments.