A more detailed description would be a good start.
What on earth do you mean with the Core Server size decreasing gradually? I doubt that the physical box is shrinking magically.
Are you talking disk-space or what are you on about? We can't help if we don't understand what the problem is - the more effort you put into a good explanation, the more likely it is we'll be able to help you better.
LANDesk EMEA Technical lead
I'm on a mobile device so can't access the file you attached.
I'm going to assume that by 'shrinking' there are fewer machines in your database.
The most likely cause for that is that they are being manually or automatically deleted when the scans become too old (check Configure - Services - Days to Keep Inventory Scans) so the maintenance is deleteing them.
With the inventory service stopping some scans must be getting rejected due to insertion errors. I would hope to see something like 'field would be truncated' in the application event log for the inventory
If this is the case you will need to extend the field size. Get onto landesk support and get them to assist in the troubleshooting. There are documents on this community that will tell you how to do this but I'm concerned at the possible language barrier and this is a dangerous change.
Thank you for your help.