Thank you! And yes, this is likely the PSU. Among other things, it provides power to the eight relays that switch the individual outlets on and off. When it can no longer provide enough power, relays will not click. In some cases they actually start clicking like crazy on and off (aka "EB832 click of death"), but the cause of this is the same.
Here's one way to tell even without taking the EB832 apart:
Take EB832 to a darker area and plug it in. Look closer at the actual outlets #4 and #8. If you can see a dim red light blinking inside, barely visible through the orange plastic around those outlets, the PSU is bad. The red light is the LED on the PSU. It stays solid red if the PSU under load is working properly, but flashes red if it's "overloaded".