I have more questions and opinions, rather than answers. If you are putting a male in with the hens for 24 hour periods every several days, isn't he getting switched back and forth from 15 hours of light to just a little light every several days? I'm not sure what time of day you are taking him in and out, but I would think that would be harder on him, than just switching him over and leaving him. And I am not real sure about the light making a rooster fertile as much as his desire would be increased (someone correct me if I'm wrong). Is there any particular reason why you don't want to leave him in with them? How old are your hens? If they are older and the male is young, maybe they are just crabby old ladies telling him no...I only say that because I have one that is doing that right now. Have you actually seen him covering any of the hens?
In November, I decided to put extra lights on two of my pens so I placed a timer that comes on at 3:30am, then goes off at 4:30pm, which still gives them a little bit of light to get to their perches so the lights out doesn't leave them in pitch dark. I don't remember how much light they were getting at the time in November, and maybe it would have been better to slowly introduce them to extra light, but I just turned it on. Within a couple of weeks, the eggs increased dramatically and I am expecting New Year's Day chicks. If my memory serves me correctly, it DID take the males a week or so to get busy. The younger male was just figuring it out with the pullets and the older male seemed to have to reintroduce himself to the hens.
Don't know if this helps.