I don't know if there's an egg-laying cycle, as I am fairly new to all this, but I have heard egg production will decrease when the days get shorter.
This has been a funny year for livestock of all sorts, not just chooks--but the subtle temperature and climate changes have caused all kinds of funky things in the world of farming. Everyone here locally whose pullets were born in April is still waiting on eggs. Maybe a few chooks here and there are laying, but this is November and most of my pullets are still not laying, even though they were hatched in April. Even my leghorn--who I got because she supposedly would start laying between 15-18 weeks of age, was in her 22nd week before she laid even one. Then she laid for 6 weeks like clockwork, was the most lovey-dovey bird, and some of you may have read her memorial on BYC--she got eggbound Monday and passed away very quickly. My EE is my only bird laying now. She is older than the rest of the flock and is about 32 weeks now, has been laying for two weeks. The rest of my flock (welsummer, RIR, BR) don't even have combs or wattles yet, and they're almost 8 months old! I know at least one other local BYCer whose chooks are a week or two older than mine, and she has no eggs yet, either. My wellie has had lots of health problems and has spent as much of her life on antibiotics as off of them, so I don't know how much longer we'll have her or whether or not she'll ever lay at all. She's the same age as the rest of the flock but is much smaller because of all the time she's spent being ill in her little life so far.
There have been a lot of posts lately (not just on this chicken forum but others, as well) from folks whose pullets started laying this year and then abruptly stopped a month or two later. I cannot help but feel it has something to do with the climate change. Seems to be a fairly common problem this year. I hope your girl starts laying again pretty soon and hope she doesn't get eggbound! Keep us posted.