If you pause the PLC program (say turn on DIP switch 4 but do not reset the PLC), does the TLServer behave normally? i.e. On line monitoring goes smoothly as usual? If so, then there is something in your PLC program that is causing the problem. Most common problem of this kind is that the PLC program writes to COMM 1 using PRINT #, NETCMD$, OUTCOMM, or WRITEMODBUS.
Second possibility is that If you have a lot of failed NETCMD$ on COMM3, especially if you run them in non-differentiated CF or have a loop that keep sending NETCMD$ command but failed, it could have taken up too much CPU time to respond to hostlink command from TLSErver at COMM1. That may make TLServer think that the PLC is not responding.
The Third possibility is if your program does a lot of SAVE_EEP command continuously, then it could result in disruption to communication. This is because when the PLC execute SAVE_EEP it shuts down interrupts in the system to prevent corrupting the EEPROM write, and some host link command characters could be lost. Continuous writing to the EEPROM should be prevented since it will shorten the life span of the EEPROM, which has 100,000 erase/write cycle life.