So everything is directly to the pump. For general filtration, how do you have those valves set?
The only way you would have some protection would be if they installed an equalizer line from the second hole in the skimmer down to a hole in the pool. If they did not, then you will always be pulling some air through the skimmer if the water level gets too low. Although if the floor valve was also open, you could hope that it keeps pulling enough water to from the floor to not destroy the pump ... but it sounds like this is not the case.
Seems like you either need to look at your pool more often and keep enough water in it or add the auto-fill and hope it does not eventually mask a leak. I would not think you should be losing enough water to drop below the skimmer unless you ignored it for a couple weeks.