Currently, no.
But, CubeCart has the ability to respect a custom API call that a "cron job" would execute on schedule, as well as hooks that could be used every time that a web page is requested to update if a specified amount of time has elapsed since the last update.
Configuring Mod Security is a server administrator's responsibility.
As best I know, Mod Security is configurable on a per site basis. Therefore, it may be the case that your other website may (or may not) have Mod Security installed, and/or configured differently.
We would encourage you to contact your hosting provider for assistance.