As well as the sharing of available bandwidth mentioned by others, the other major limit to the number of active connections on a single wireless AP is caused by the fact that the connection is not "switched" (it can't be as the devices don't have dedicated transmission lines to the AP). When a device picks up that a packets it sent did not get through, do to interference from other devices sending packets at the same time or due to outside interference, it will hold back a random fraction of a second and try to resend them. As you increase the number of devices the chance of interference due to two devices transmitting simultaneously rises significantly until it gets to the point where each device spends most of its time waiting to resend packets that have not got through (which may cause time-outs and make it seem like the wireless connection is not functioning at all).
For more than a one or two tens of users it is recommended that you spread the load over more than one AP on different channels, or you can use the same channel if they are spaced far enough apart, though this is often not practical for a number of reasons.
I would not expect this to be a hard limit though - you would see increasing performance degradation and not s straight cut-off once a certain number of active devices are present.
Do all your devices stop being able to transmit once you hit your limit, or just the most recent ones to join the access point, or just selected devices seemingly at random? If not all devices fail at the same time then you may have a fixed limit somewhere, but you'll need to check the documentation for the device for specific details. The limit may also be elsewhere - do you have a simple firewall device between the wireless access point and the rest of the network?, if so then this could be the location of the limitation instead.
If you are seeing mainly the devices that are furthest away having trouble, then I would suspect it to be the congestion issue described above with the furthest-away devices suffering most as their signals are more likely to be drowned out by transmissions from closer devices when their transmissions collide.