One reason for LinkLogic to either not export or stop exporting messages is the LinkLogic filename counter has been reset to 0 or null.
Log into Centricity and navigate to Go->Setup->Settings->LinkLogic->Defaults for EMR or Administration->LinkLogic->Defaults for CPS. Then check the "Prefix characters for export file names: Counter" If this is set to either Zero or Empty then you should change it to a number higher 10000.
This settting colntrolls the number part of the file name on all messages exported. Once LinkLogic has exported files equal to the number set Centricity will reuse the numbers as part of the file name again. So the number should be higher than the total number of messages you would expect to export for a given day so as to not duplicate file name for a given day.