If you do live in the same area and you have not seen the sponsored post about your lost pet, Facebook has likely decided that another business’s ad is more relevant to display to you at that time (how ads work). Each individual sees different ads based on their interests, but with people checking their Facebook page an average of 14 times per day it’s not something to worry about. If you would like further verification that your ad is displaying in the target area, please contact our support and we can provide you a screenshot from our Facebook Ad Manager account.
Other factors that can cause you not see the Sponsored Post in your news feed: Facebook has not yet approved it, you’ve already engaged with or seen it today, you’re not seeing sponsored posts at all, or Facebook does not believe you live in the area (possibly connecting from proxy or instagram/facebook profile says you live somewhere else):
https://www.facebook.com/business/help/224325004246343