All my collectors are going down every 24 hours.

Just a few random thoughts..

Do the agent start stop times coincide with the Application log events ? Are there patches pending installation/reboot. This can kill machine performance. If you manually spin the LM service does it take as long to reconnect ? What happens in wrapper.log after a service spin. Is your firewall blocking one of the LM endpoints, that was a fun one to solve. Is the FW setup as company.lm.com or just lm.com