ISP controls the number of devices which can access internet
Some ISP will set a fixed number of devices, say 5, which can connect to the router and access internet at the same time, the sixth and other devices can connect to the router but can't access internet regardless to whether one or more of the five devices have been disconnected or turned off, unless the router is rebooted.
When rebooted, all devices can connect to router and will access internet on a “first come first serve” base but only five can succeed in accessing internet.
Is there any method to increase the number of devices which can access internet?
I don't think ISP can control number of devices behind the router as the source of data (say data from your device) is transparent in ISP view unless, the router itself is compromised by ISP so that the ISP can obtain device list behind the router.
I would say your problem appears to be the matter of settings in your router