The HA-1 has several protection circuits that shut it off if it detects anything wonky with power or connections. It's got them on the power supply, and on the 1/4" headphone jack, among other places. These relays are sensitive and sometimes trigger for no apparent reason. The HA-1 doesn't need a lot of power, but it likes clean power and will shut off if it detects instability.
For example: when you plug a headphone into the 1/4" jack, it triggers a relay that shuts off the balanced headphone output (but keeps the HA-1 powered up). This 1/4" jack also has a protection relay that shuts off the HA-1 entirely if it detects a short circuit. Sometimes this relay triggers for no reason even with nothing plugged into it, and the HA-1 suddenly shuts off. When this happens, it helps to exercise the relay a few times to reset it.
While the HA-1 is off, plug in a 1/4" headphone jack. Power on the HA-1. Wait a moment for it to power up, you'll hear relays click when it's ready. Unplug the 1/4", wait a moment and you'll hear a relay click. Plug it back in, wait a moment for the relay click. Do this a few more times to exercise the relay.