The maximum device limit will depend on your router’s capabilities and your internet service plan. There may also be a setting that limits the number of devices able to connect.
Most of the wireless routers and access points state they can support about 250 devices connected at once. However, this doesn’t mean that because you can theoretically connect close to 250 devices on a single access point that you should do it. You also need to consider that every device connected to your network is likely to decrease the available bandwidth to other devices that are on the same network. The reason is that all these devices will not only be sharing the same wireless network but also will share the same internet connection supplied by your broadband service provider.
For help with Wi-Fi troubleshooting please read How to Troubleshoot Wi-Fi Connectivity.