Diagnosis
This is almost always a power issue. The Alien's power supply is a known weak point and can get flaky, especially if it's been warm or you're using a long extension cord.
How to Fix It
First, let's rule out the wall. 1) Unplug the router's power brick from the wall outlet. 2) Plug it directly into a different wall outlet—no power strips or surge protectors for this test. 3) Make sure the barrel connector is pushed all the way into the router until it clicks. Give it a solid push. If the random reboots stop, you've found the culprit was a bad outlet or a weak connection.
If That Didn't Work
The power supply itself is likely failing. You'll need a replacement. It's a specific 48V 1.25A Gigabit Power Adapter with a barrel plug. Contact Ubiquiti support for a warranty replacement or order a genuine one. Don't use a random power brick; the voltage and amperage need to be exact.
Heads Up
While you're checking connections, also make sure the router has plenty of space around it for ventilation. These things put out heat, and overheating can look like a power problem too.