It's not a mystery, it can be analysed.
Waited for exactly a year for a Year 1 in year admission at an oversubscribed school (also my closest) .
Truth be, I only really stuck it out as I was overcompensating for my children not having a father in the home and having already moved my children house 4 times in 6 years, I was determined to find some stability that a small school, with it's reputation, and it's wraparound care facility, linked Junior and Secondary schools priority, and proximity to my immediate future work needs, could offer.
Bounced around from mid twenties down to two.
There's online stats out there and if you can analyse them with the other publicly available school allocations data, you'll find a pattern, as I eventually did, of when and why the waiting list fluctuates. I even found out who the other children were on the waiting list when we reached number three, but that may be down to circumstance - one of them was a family just moved in a few doors down from abroad and as they were a few doors closer to the school they got in. We saw the child in the playground.
Bizarrely, number two on the list was also from the same school as my child (village 5 miles away).
Ultimately, we either got in through sheer daily doggedness - ringing the admissions team daily (because list mobility can change daily), I wrote pleading letters to the various 'secret' departments such as Education Entitlement, requested an Education Welfare officer involvement, wrote to both head mistresses at each school suggesting they discuss our situation together and how a transfer could benefit both schools, hinted at the extra funding new school would receive by accepting my child under the Pupil Premium scheme and how that could waive the class size limit, and so many more suggestions and carefully worded pleas, all this after the failed Appeal of course.
Eventually we got our transfer, whilst aware that number one on the list still fulfilled the admission criteria that we didn't. That child is still at the same old school.
It coincided way youngest starting Reception at the new school. But younger sibling is not an admission priority. But being aware of the nooks amd crannies of our situation with two children at different schools, amd the personal involvement of the Education Entitlement officer at the end, who I phoned several times a day, we got the transfer. These last two factors may have helped. Or may have not.
Everyone around me thought I was ridiculous for sitting on this, to the detriment of certain people who assisted with the complicated logistics involved in transporting my child to her old school, detriment of my daily stress levels over the issue. When I could so easily have popped my child into the (third furthest away but with spaces) school and it all be over with.
Having enjoyed an exceptional Catholic ex convent education myself which my mother engineered from infant school age, making us walk 50 minutes to primary school in order to get the linked secondary school priory (itself a 40 minute bus or train journey to the next town), rather than packing us up off the lane to a rural primary ten minutes walk away, my fate was probably set on this course of action.
I spent a year in total disarray and stress, researching and following up every lead and opportunity, analysing data, recommending, suggesting, hinting, pleading between education and child welfare departments and the two heads themselves.
A good education is all I can hope to offer my children to make up for the lack of traditional two parent family life or home stability or income. It was worth it in the end.
Summarily, to answer your question, don't just apply, appeal and give up. Grow a journalist's nose for unearthing every hidden and visible route in and out of the situation, finding all leads and then some. You can fight the system if you don't give up. Good luck.