In later versions of Splunk (not sure when it changed), you have to use the Add Actions button and select the Add to Triggered Alerts alert action. Perhaps one of your Search Heads is an older version of Splunk or perhaps it is configured in such a way that this action is always auto-added. In any case, you should be able to manually add this to the ones that don't have it.
By the alert not trigger, what exactly do you mean? If you look at jobs, does it show up there? Or just that, say, it won't send you an email? Because for the latter I'd check for differences in email setup between the two, AND check that whatever you are relaying through has allowed both servers to do this.