If the data source to your CVC4 (whether PLink or DMX) stops while the CVC4 remains powered (i.e., the DMX controller happens to lose power while the rest of the install remains powered), the CVC4 will continue to output to your constant voltage lights based on the last frame of data it received before the dropout.
For example, if channel 1 of the CVC4 was at 50% intensity before the data dropped out, the CVC4 will continue to hold this output level until the data source comes back online and sends new levels.
The CVC4 only changes state when it gets told to or is power cycled.