If it is across multiple devices that are reading full signal strength, definitely router or model side. When the internet drops, most modems have a status LED for US (upstream), DS (downstream), router connectivity and finally 'online/internet'. If the online/internet led (if your device has one) is out, then the problem is in your modem, building wiring or external. If all the lights on the model are lighted, try replacing the cable from the modem to router.
Also, when your internet goes out, does your router feel very hot/abnormally hot? Dust buildup can create heat buildup which can wreak havoc in any device.