I had a leak in my valve box and I was surprised the system continued to work while completely under water.
Anyway, I discovered the water supply connection to the valve was leaking. After the leak was fixed, its fairly dry in there.

My point is, can you determine the source of your water in the valve box? It seems by keeping it dry in there, the system works fine.

If you are comfortable using a volt meter take and check the ohms on valve solenoids that don't work. you should be getting around 25-40. If it shows 0 or a very high number then the solenoid has gone bad. If you don't have a volt meter that is fine take the solenoid off of the valve that is working and put it on the valve that is not working if the solenoid is bad then it should come on but if it is bad then there shouldn't be any change, unless the wires are bad.

Here is a link that might be useful: do_it_your_self_web_site

I have a hunch that the wire's insulation is nicked, and that when the soil is saturated, it creates a short to ground. The volt meter check should be done with the area both wet and dry; I suspect you'll get a reading over 500 ohms when wet. It doesn't sound like the valve box is actually flooding and creating a short there, but bare wire nuts or exposed wire can cause the same syptoms.

The solution is to fix the nick, which can be difficult to find, or replace part or all of the wire run. If your sprinkler guy has a wire tracer, he can mark out the wire path, I doubt that the nick will show up. (There is a device called a Pulser that can find ground faults, but few people have access to them. Some irrigation suppliers rent them out.) Once the wire path is marked, check it to see if you may have done any planting or digging along the path. That would likely be where the problem is. If that's not it, you'll need to run new wire.