Based on my experience, I strongly recommend getting your LO a sleep study. My DH was initially diagnosed with sleep apnea and placed on oxygen because his blood oxygen levels were going down to 88 during his sleep. That was 2 years ago. Over time, as my DH started having more trouble with sleeping, we had another sleep study done and discovered that he has Central Sleep Apnea (not the common Obstructive Sleep Apnea that most people have). The critical piece of information is that sleep apnea can cause your LO to experience brain damage if the oxygen saturation levels go down into the 70s. The sleep study we did last year and more recently indicate that my DH's oxygen saturation levels went into the 70s even on the machine if he is on it without oxygen. Oxygen sats in the 70s can DEFINITELY cause brain damage.
So far, there's no clear connection between dementia and sleep disorders (other than REM sleep disorders that come with Lewy Body Dementia); however, if your LO is having apneas during sleep that is causing the oxygen saturation levels to drop into the 70s, then you are losing more of your LO than is necessary. It is at least worth exploring and is covered by insurance (including the oxygen and apnea machine - for my DH, a VPAP).
I noticed that my DH moved a lot during the night and was very sleepy every day. He had snored, but the #1 issue was his sleepiness during the day time. He has been on medicine that causes sleepiness, but the sleep study was covered by insurance so I went ahead and had him checked. At first, we determined that his oxygen saturation level went below 88% during the night. O2 sats should not be below 94, though some doctors will not do anything for low 90s. All doctors agree that O2 sats below 90% requires oxygen. At first, all we did was put my DH on 02. After about 5 months, I noticed that he was continuing to decline and decided to get him fit for a CPAP (continuous flow). That required another sleep study. The 2nd sleep study is the first time he was diagnosed as having central sleep apneas. Apparently, when you use a CPAP on someone with central sleep apneas, they experience an increase in apneas instead of a decrease. My DH actually uses what they call a VPAP, which is an external ventilator. It is a very sophisticated machine that tracks his breathing pattern and forces air when he stops breathing. Over a year after being on the VPAP, I am convinced that he would not be as present if we had not gotten him on the VPAP. The neurologist agreed that my DH might not even be alive if we had not gotten the machine. By the grace of God, my DH was able to be alive and aware enough to understand what was happening when we had our first grandson.
Knowing what I know now, I would have had the 1st sleep study include checking for a CPAP. I noticed that his rate of decline slowed after we got him on the VPAP.
I am not saying this is a cure, it isn't. However, it has helped avoid the additional loss of cognitive and other functions that would have resulted from insufficient oxygen. His quality of life and ability to participate in life is much much higher than if he had suffered brain damage due to oxygen deprivation during the last 2 years. Protecting what he has left is key.