Some customers report, that their Agent goes into gateway mode, despite that the core is pingable.
To determine if the agents need to get into gateway mode, it will check if it can get an http reply from the core. It actually tries to get http://[your core]/ldlogon/lddwnld.dll. If the Agent gets a http 200 OK it knows that the core is accessible and will not go into gateway mode.
The Agent will only check if either the IP of the machine changes, the user logs on or the LANDesk services get restarted. If none of these triggers happen the client will stay in the current mode.
Check why there is no access to the http URL of your server. It might be a firewall in place.