I am experiencing the same phenomenon since installing Little Snitch about a week ago. However, the "network outage" seems specific to Safari in my case. Other apps appear unaffected while Safari's network response time falls off a cliff. Additionally, I can launch the Safari Developer Preview and browse w/out networking issues while the main Safari app is experiencing this phenomenon. Just like you describe, the response time returns to normal after about 5 minutes or so. During this phenomenon, iStatMenu's CPU monitor reports both Safari and Little Snitch around 50% utilization of my 4 cores. Fans spin up, battery drains.. it's ugly. I'm using Little Snitch 4.1.2 on macOS 10.13.5. I've uninstalled Little Snitch in order to see if the issue persists.