About 5 hours.
Half life of narcan is 1 hour. At five half-lives, or 5 hours, the initial dose of narcan is 97% eliminated and if the patient has not required another dose of narcan for recurrent respiratory depression by this point, it is probably safe to discharge the patient home.
Source
Naloxone: Drug information. Lexi-Comp
Image source: http://www.nes.scot.nhs.uk/prescribing/topics/TDM/fig2.gif