Limited number of users with Firebird Classic server?
Firebird Classic is run via xinetd or inetd which have their own configuration and access control.
If you use Inetd, check the file /etc/inetd.conf and find the line starting Firebird server (usually the one starting with gds_db). The value in 4th column on that line is something like 'wait.30000', where 30000 would be a number of instances of Firebird server that can be started within an interval of 60 seconds. This setting is used to prevent DOS and DDOS attacks on the services.
If you use Xinetd, there are the default settings in /etc/xinetd.conf, and per-service settings in /etc/xinetd.d/firebird which override them when present. Check for 'instances' variable in both of those files as they determine a total number of server instances that can run simultaneously. These settings are used to control the server load.
If you use a terminal server, have a web application or any other setup that might cause connections to originate from the same source, take a look at 'per_source' setting as well. It limits number of connections coming from the same network host.
When client tries to connect and limit is reached, it would get an error like this one: Connection rejected by remote interface.