Since you can see the module in NetEdit, this just means that the Ethernet side of things is working. I also venture to say since your Modbus TCP communications is continuing to work that the PLC side of things is also working.
Some questions:
(1) Your question revolves around using just 1 H0-ECOM100 for the Modbus TCP mastering and connection to DirectSOFT, right?
(2) Does installing the 2nd H0-ECOM100 for a dedicated DirectSOFT link fix all the issues?
(3) In NetEdit, does the CPU Test pass for the 1st H0-ECOM100?
(4) What error do you get in DirectSOFT when you try to make a link to the 1st H0-ECOM100?
It also may be interesting to find out exactly what is going on on the network as a whole by using Wireshark (free Ethernet sniffer) to log a sample of the telegrams when you are trying to make a link. Of course, this would require a hub (not a switch) for the sampling.