Ethernet Problem

I am working on a project for the Panama Canal Authority.
We already have two master plc's in a BCM scheme ( 1785-l80E), but we have a lot of slaves almost 80.At the beginning there were no trouble at all, cause we were puting the machinery in service one by one, but now that we have all the slaves connected our message instructions send an error code : " already at maximum number of connections". After that we decided to launch the MSG instructions just when there were something to tell the slaves, and it worked.Only problem right now is that our slaves must report status to the masters, then we have programmed MSG instructions in the slaves to send the data to the plc-5/80E , but it seems there are a limit of MSG that can target the master plc cause the first 12 ones worked out fine, but after that all of them showed a message error saying connection broken.
Can somebody tell me how many MSG instructions coming from different slaves can target a plc-5/80E Ethernet port ?

I'm about to over-use a particular word

A PLC-5E controller can support 64 TCP connections.

For "CSP" protocol (used by older PLC-5E and SLC-5/05 controllers), each CSP application connection requires a TCP connection. For ControlLogix peers, that's not necessarily the case; more than one ControlLogix CIP application connection can use the same TCP connection. But at least it's going to be 1:1.

You can go to the built-in Web page in the PLC-5E and read the number of Application Connections.

Each MSG that goes from the PLC-5E to a remote device on Ethernet is going to establish and keep open a TCP connection.

Each MSG that comes from a remote device to the PLC-5E is going to establish and keep open a TCP connection.

Each RSWho browse that connects to the PLC-5E is going to establish and keep open a TCP connection.

After you send an MSG, the TCP connection stays open for a default of 30 minutes.

I'm not sure how you're going to support eighty remote devices with a PLC-5/80E controller. You can set up the PLC-5 to both Read and Write from that remote device, and that would reduce your number of connections by half. Or, you could set the Inactivity Timeout to some value less than 30 minutes and just deal with the delays for TCP connection establishment in ladder logic.