An oxygen saturation of 65 to 70 is abnormal under any circumstance; awake, asleep, resting or with exercise. The cause could be respiratory, such as obstructive or central sleep apnea, or cardiac, such as cyanotic congenital heart disease. It could also be that your oximeter is giving erroneous results. If these low levels are confirmed or validated, you should begin with a sleep study, in a sleep laboratory.
Does your doctor know this?
I think that is a VERY low O2 saturation. If your doctor is aware of it, and is okay with it, that's fine.
Even if he knows about it, though, I would remind him from time to time that it's still low. He may be able to tweak your treatment a little.
That is a very low oxygen saturation, , your doctor did a sleep study on you I suppose?? May need BIPAP OR CPAP macine to raise your O2 sat while asleep. Are you talking about actual oxygen level or per cent satuaration