Consider also that the fish are not the only things consuming oxygen in your tank. Nitrifying bacteria and algaes will consume oxygen as well. Further, at night (when this skimmer died incidentally), some algaes will breath and consume oxygen contributing to the oxygen depletion.
Also, oxygen saturation will occur somewhere between roughly 6 and 8 parts per million in a saltwater tank while this number ultimately depends upon temperature, salinity and elevation. Temperature has the most effect, higher temp means lower oxygen holding potential of the water as outacontrol mentioned. This means that the water molecules have absorbed as much oxygen as they can easily hold under the present conditions. Any more oxygen added will be released back into the atmosphere.
Ultimately you have to get oxygen into the tank somehow. It doesn't have to be a skimmer, or an air stone, or a powerhead, but something has to add oxygen to the water. If the tank relied on one source of oxygen (whatever that source was) and that source happened to go and your tank was now consuming more oxygen than what is being added, you can reach a point of deprivation.
Occam's Razor.
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