When you remove the lid you also disturb the co2 that was built up inside of the fermenter, which allows oxygen to get in. I only check final gravity on bottling day. If I have any doubts that it might not be finished fermenting I take it out of the swamp cooler for 2 days to let it warm up and finish off. As it warms up (and finishes fermenting) it releases suspended co2 which will scrub out any oxygen I might have let in during the previous gravity reading.
Bier war sein letztes wort dann trugen ihn die Englein fort...