A recent article in the journal Neurology, from 1/31/17 studied sleep in individuals over 65, with and without cognitive impairment (memory loss). It was found that individuals with cognitive impairment had worse sleep quality. In addition, individuals with cognitive impairment had a higher risk of having sleep apnea and more frequent drops in oxygen levels during sleep.
This study is not conclusive and does not prove that breathing issues in sleep cause dementia or memory loss. However, it is a piece of evidence that suggests there can be a link. The concern is that chronically low oxygen levels in sleep (and other effects of obstructive sleep apnea) could affect the brain long term, contributing to a risk of sleep apnea.