Greetings cosme161,
Thanks for visiting the Apple Support Communities! I understand you need to power cycle your iPhone to use the Internet.
Is this happening while your iPhone is connected to Wi-Fi or cellular data? If this is happening while connected to Wi-Fi, then let's have you restart your router and cable or DSL modem, and then test the behavior. If the issue persists, let's have you reset the network settings on your iPhone. Keep in mind, this will also reset the Wi-Fi networks and passwords, cellular settings, and VPN and APN settings that you’ve used in the past. You can see those steps outlined in the following support article: If your iPhone, iPad, or iPod touch won’t connect to a Wi-Fi network - Apple Support
If further assistance is needed, it would be helpful to know if you've tested the behavior while your iPhone is connected with a different network: Connect to Wi-Fi on your iPhone, iPad, or iPod touch - Apple Support
Kind regards.