You can add an expiration date and time to the settings of any product. Once the time has passed the product will be considered "unavailable" or "out of stock."
Note that all time settings correspond with our server time here in Arizona. Arizona is Mountain Standard Time but we also do not follow Daylight Savings Time at all so we're a small island of consistency where everyone else changes their clocks twice a year. Right now we should be in line with the rest of Mountain Standard.
Also note that the expiration time is on a 24 hour clock rather than tracked by AM/PM, so 12:00 is noon and midnight is 00:00.
That's just a passive limit that you can set within your product though, the expiration date will not be posted on your website anywhere unless you also post the date there, or some sort of animated countdown of your own devising.