When a host check goes into a failure state (WARN, CRIT), the other service monitors on the target element will have their alerts and/or actions suppressed and enter an UNKN state until the host check recovers.  There are a number of scenarios in which you may still notice alerts being sent for the non-host check monitors:

 

 

As a general rule of thumb, your host check should check as often as the most frequently checked service on the element and have a recheck interval / max rechecks that is shorter than the most frequently checked service.