Why does this happen? Why does sometimes the on the Admin Kit, a client is not visible for a couple of day and the "Computer Status Message" state that the "Host is out of control" or "Real Time Protection is not running". But when I go to that specific client, the Kaspersky is running and updated. Why is this happening?

How can we avoid the clients to disconnect to the Admin Kit?

Hello,

What type of network it is ? I mean, if your workstations are connected to the Administration Server through a VPN, a standard local network, Internet, ...
Also run klnagchk utility from a problematic computer and paste the report here.
Finaly precise what version of Administration Kit, Network Agent and Anti-Virus you are using.