Apple products not picking up Internet from wi-fi router. Why?

I recently had someone over my house who brought an iPhone and iPad and gave her the passwords to connect to my wi-fi signal. But I also had my iPhone and iPad connected.

Three of the devices connected, but only after I unplugged the wi-fi router and replugged it. But I couldn't get her iPad (which is 1st gen) to connect to the Internet.

In fact I typically need to reset the router for her iPad to connect. So why is my router having this trouble? When I go to the nearby cafe, everyone's connected to the free wi-fi. So what gives?

Some wireless router has limited number of device that can link up with it. Remember the old wired router and hubs? Remember how they are limited to the numbers computers that can hook up to the ports since there are so many ports on that hub?
Wireless routers are the same. They can only handle so many devices at once. If too many devices are linked with them, they will have connection issues.
The wireless hub at cafes and Wi-Fi hotpots are commercially made to handle more connections than the typical residential wireless router. Check your router manual or the manufacturer's website for the information on your router's capacity.

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