Reread the post again and had another thought. Does the ControlLogix (& I assume you mean the large 1756 series, not CompactLogix) have any Ethernet based I/O communications? This can include variable frequency drives, input/output modules, motion controllers, etc.
If so, and you are communicating through the same Ethernet port as is being used for the Ethernet I/O you can definitively have a problem. There is a little bit of work someone needs to do (none of it major) to make all that work.
Depending on I/O updates and quantity of I/O on Ethernet you may need to upgrade to a managed switch that includes IGMP Snooping. Next, if there is not another Ethernet module in the rack dedicated for HMI/data collection comms, it needs to be added. If there are no available slots in the base rack then you should upgrade your Ethernet Module to a 1756-EN2T.
Also, depending on your controller firmware revision and the Ethernet module firmware revision you may be able to just update the Ethernet module firmware. If it is older then I think V3.5 there was an issue with TCP communication timing that could take down the I/O UDP based communication (that is where the recommendation for separate Ethernet modules stems from). Anyway, like alluded to a post above, not much information to go on to help.