A systematic review of the side effects of retainers said nothing about sleep related side effects, so they probably are not a significant problem. There are a few related studies that look at an assortment of othodontic treatments and how they affect sleep. I've included them below. An orthodontist would be able to give a more concrete answer.
Also, note that some types of retainers are actually used to treat sleep apnea and related sleep issues (see this for example).
TLDR; Orthodontic treatments such as braces and and retainers can, in general, affect sleep and sleep quality (for good and bad). However, there seems to be little direct research into what specific sleep related side affects retainers cause.
From https://www.ncbi.nlm.nih.gov/pubmed/24554561 (I think this one was looking at braces)
The subjective parameters taste,
dry mouth and breath odor did not show statistical
Quality of sleep:
Impact of orthodontic appliances on sleep quality:
CONCLUSIONS: In young orthodontic patients, there appears to be no difference in sleep quality with or without the overnight use of these appliances after they have been worn for a minimum of 3 months.
However, contradicting that study is this one:
Impaired sleep the most rarely
occurred for patients treated with removable appliances
(40.6%) and braces (51.1%) and the most
frequently for patients treated with functional appliances
(85.7%) and braces, and head gears (88.9%).
There's no evidence that I'm aware of that retainers (or other orthodontic retainers) cause sleep apnea. Similar devices are sometimes used to treat it, though.
However, people who need braces, retainers, etc. may be at higher risk for it. From the intro of an ape study apparently conducted because of similar complaints:
Oral respiration associated with obstruction of the nasal airway is a common finding among patients seeking orthodontic treatment.