Yes, you will probably lose your internet during a power outage unless you have backup power. Power outages are the most common causes of internet outages during storms, followed by rain. Your laptop might be fully charged and have battery juice for hours, but most modems don't have a battery backup. Plugging your computer directly into the modem with an Ethernet cable wouldn’t solve the problem either. If you have a generator or power bank, you could plug your router into that to maintain your signal.