Hi Alessandro,
It should not matter if you start/stop PCo on a schedule. Most customers leave it running 24x7.
Note that stopping a PCo Agent Instance from a task scheduler that executes the Net Stop command does not do anything different than stopping an Agent Instance from Management Console -- both stop the Agent Instance Windows Service. Please confirm this by starting and stopping PCo through Management Console and while started, execute a tag browse from MII before stopping. If you see a different behavior with this test please let me know along with the pertinent details (Log Messages, etc.).
Regards, Steve