Simple host monitoring solution
Solution 1:
Zabbix is still one of your best options, you just have to invest more time into configuring it. It offers autodiscovery with templates to configure the monitored services and alerts.
It is also self-hosted, free and open-source.
We monitor with it hundreds of machines and it has never failed us.
About the dropped agent -> server connection, you should check first if your server firewall allows port 10000 inbound for the agent connection, then on the agent configuration if the Server/ServerActive directive lists the server IP address.