Little Snitch automatically turning filter off?
That's its demo behaviour, it will run for 3 hours then switch off.
Check it thinks it's authorised.
'Open Little Snitch Preferences...'
Registration tab
Also, as you are running it on 2 computers, ensure you have a separate Registration for each [or a Family License] otherwise if it sees 'itself' on the network it will switch off.
You are correct in your assumption that it is not applying the Rules when the Network Filter is off.