Respiration rate (RR) dynamics entrains brain neural networks. RR differences between mild cognitive impairment (MCI) and Alzheimer’s disease (AD) in response to oral appliance therapy (OAT) are unknown. This pilot study investigated if RR during stable sleep shows a relationship to pathological severity in subjects with MCI and AD who snore and if RR is influenced following stabilization of the upper airway using OAT. The study cohort was as follows: cognitively normal (CN; n = 14), MCI (n = 14) and AD (n = 9); and a sub-population receiving intervention, CN (n = 5), MCI (n = 7), AD (n = 6) subjects. The intervention used was an oral appliance plus a mouth shield (Tx). RR maximum (max) rate (breaths/minute) and RR fluctuation during 2116 stable sleep periods were measured. The Montreal cognitive assessment (MoCA) was administered before and after 4 weeks with Tx. Baseline data showed significantly higher RR fluctuation in CN vs. AD (p < 0.001) but not between CN vs. MCI (p = 0.668). Linear mixed model analysis indicated Tx effect (p = 0.008) for RR max. Tx after 4 weeks lowered the RR-max in MCI (p = 0.022) and AD (p < 0.001). Compared with AD RR max, CN (p < 0.001) and MCI (p < 0.001) were higher with Tx after 4 weeks. Some MCI and AD subjects improved executive and memory function after 4 weeks of Tx.