MF286A turns off every 10 minutes when running on battery. That doesn't happen when powered from the grid, also didn't happen on stock firmware (well, maybe it had occasionally once or twice). Doesn't depend on load nor battery level. Pressing WPS button makes router to power on again. Seems like some powersave scheme in hardware...
Just tested: same if I halt booting sequence via UART and just wait without actually booting anything.
So it's not like OpenWrt causes this behaviour, but like stock firmware had something to prevent it.
Is there any way to turn off this powersave, or maybe perform some action every 9 minutes to reset the timer?
So you're [actually] saying it's unrelated to stock firmware too, given the fact it also occurs when nothing was booted.
That may be default behaviour of hardware. BUT stock firmware seemingly has some workaround to change this behaviour (that workaround may have failed once, but still).
If this is the case, then it is related to stock firmware.
While on the stock firmware run cat /sys/kernel/debug/gpio and copy/paste the result.
Try to find scripts in the stock firmware that work with GPIO.
What was described appears to be similar to the hardware watchdog timer present in some devices.