Do you get any errors from your clients? Or only when you try to inventory scan the core?
From the core when you go to configure services and look at the Inventory tab, are you scanning the server at a specific time? And if so are you seeing any errors in the event log during that time or if you look at the "last updated by inventory server" under your cores inventory does it show it's scanning at that time?
By default your core does not get a standard LANDesk agent on it as part of the core install, this is something you have to do after. I would make sure all the LANDesk services are running and if you did install an agent on your core, maybe try reinstalling it.