It is usually something quite common when important changes are prepared in iOS or Mac, since Apple performs maintenance tasks or simply tests in its application stores or in any other service that it offers us, such as iCloud, iMessage or Mail. for this cause or simply for a problem with the service, App stores for all Apple platforms, be it iOS, tvOS or macOS (OS X) have been inaccessible to users around the world for a while, preventing updating applications, performing searches or downloading new applications. Although according to Apple the problems have already been solved, it may be that there are still users who have this problem and cannot access any of the stores, so stop restarting the router because it is not your problem.
At any time you can check the status of any of Apple's services from this link. Right now, as you can see on that page, all the services are active, without having any problem at least recognized by Apple. The problems of access to the App Store have occurred between 13:45 and 15:45 today (Iberian peninsular time), and have occurred all over the world at random. As we say right now there should be no problem according to Apple.
The new operating systems that Apple introduced us in June will debut next week. Therefore, these problems are likely to recur during these days., so that you do not go crazy looking for where the problem is, if any of Apple's services is suddenly inaccessible, better go to the page mentioned above where we will see all the updated information about their services. If there it appears that everything should work correctly, then you can start restarting the router.