There are two reasons why your Terminals are offline. Firstly, it could be your connectivity issue; secondly, it could be that you have other computers that have installed STAMS and set it as the Listening machine. Please follow the steps as follows to check if there are other computers set as the Listening machine:
Go to the STAMS.
Click Tools and select Advanced Configuration.
Click the Network tab.
Check if any other IP address is set to Listen mode. (Check with your IT whose this IP address belongs to)
Select Auto and click OK.
Exit STAMS and log in again.