"Můj manžel zase spí."

[Samaelch]

Why can't I use "My husband sleeps again"?

[kacenka9]

Because he, obviously, is in the process of it, right? otherwise you would not have the 'again' in there. And as such you need to have continuous tense

[Zeego1]

And why not "My husband is asleep again"?

[ErinLachs]

"my husband is asleep again" was not accepted...