Say you have two triggers:

T1, referencing item I1 on host H1,
T2, referencing item I2 on host H2,
T1 depends on T2.

If H2 is disabled, then T1 will not recalculate even if I1 receives new values.

I have "fixed" this by removing the dependency, waiting for zabbix to recalculate T1, and then adding the dependency again.