I think what you are needing is two comparators (or one and a zero crossing detector) with the first one acting as an enable signal for the second. If I understand, if the gate is above a certain threshold, it allows the zero crossing detector to trigger a monostable (in hardware or software) and generate a pulse. It the gate signal is too low, nothing happens at all. Is this correct?
Another question: if the gate signal stays high for more than one zero crossing, should another pulse be generated or should the circuit inhibit after the first pulse?
The term 'zero crossing' suggests the signal will have a positive and negative part, do you need it to handle both or will any voltage close to zero, regardless of polarity be OK as a crossing point? I'm thinking that if all you need is to know when the signal is very low, you may be able to use a bridge rectifier so the polarity is always the same, it simplifies the electronics that way.
Brian.