WordPress causing host server to crash

Hi,

my WordPress caused a a server crash last night. My host says his log file is filled with entries such as this :

[mod_security: Filtering against POST payload requested but payload is not available [hostname “www.domain.com”] [uri “/folder/wp-admin/admin-ajax.php”]

The server crashed once the log file became too large.

My host partially solved the issue by disabling the logging of entries regarding PAYLOAD, but he complains about the fact that the file admin-ajax.php sends a request every second, causing unnecessary CPU usage.

I used to sometimes leave my computer logged into WordPress overnight. My host says I need to stop doing that.

What can I do to stop WordPress from being such a burden on my host?
Is there a way to slow down the rate for these requests? Is there a drawback to doing this?

The theme I use is Frugal (last version).

Thanks in advance.