How to operate automatic sprinkler system anti-siphon valve
The type of anti-siphon valve you are likely using is not intended be constantly under pressure. It is not intended to have down stream valves actually controlling flow. It is meant to only be active for the duration of an irrigation cycle, then to have pressure removed when the sprinklers are turned off.

The proper device in this situation is a reduced pressure backflow device. It is much more expensive than irrigation anti-siphon valves, but it can serve many stations instead of installing a basic anti-siphon valve for each station. It also allows more flexibility in control valve placement because you don't need an anti-siphon valve sticking up after every valve.

Yes, you could just run out and turn on the main valve before the sprinklers cycle, then turn it off when finished, but that defeats the purpose of having an automatic sprinkler system.

How do I know all this? I did the exact same thing and had the exact same problem!