Ds got into a good, over subscribed school because we live right next to it, in a house we rent. He's just started reception. Dp has inherited some money and we are now in a position to buy a house which is great, we've found one we love but it's 15 mins walk from the school. Not far but it means that ds's new school is by no means the nearest one. I know there's been a lot out stuff in the media recently about people renting or buying houses within school catchment areas just to get their child into a good school and a lot of outrage and I'm just a bit nervous that we'll get in to some sort of trouble for moving away when ds has only just started school. They can't kick him out can they? I'm not keen to bring this up with the school just yet in case it is a problem!
You wouldn't lose the place but if you have other children you would be wanting to get into the school at a later date you would probably have problems as you would be an out of catchment sibling. As far as I know once you have a place and the child has started they can not withdraw (unless they prove it was a fraudulent applications to start with), how long had you lived at the rented address before you applied for the school? If it has only been a few months then it is possible they may question it but at this stage that is highly unlikely. If your ds is an only and you have no plans for more then all should be fine.
Now that he has started school the only way your son's place can be taken away is if your original application was fraudulent. As Roadkillbunny says, if you have only lived at the rented house for a short time this may lead to questions but you shouldn't have any problems provided you can prove to the LA that the situation is genuine.
Whether or not you will have problems with getting any future children into the same school depends on the admission criteria used by the school. Of course, they may have changed by the time this becomes an issue so this is a difficult one to judge.