In general there are several reasons why an item might not appear in a given search.
Too soon -- items can take 24 hours to be indexed and appear in a search; longer if your revise the item before it appears.
Sorting by "price plus shipping: lowest first" -- when a lowest first sort is performed, you will often see a message at the top of the results: "We’ve streamlined your search results to show you the best listings. See more results" -- if you want to see all the results, you need to either try another sort, or click on that "View all results" link. Otherwise you are only seeing a subset of the results of that search, despite the number that is shown at the top. Try counting the results before and after following that "all results" link.
Wrong Category -- if a site-wide search using a particular keyword returns many items, eBay will often direct that search automatically into one particular category. Sellers should take this into account when deciding which categories to list their items in. If possible, try searching the way a potential customer might, and see where the search ends up.
No Shipping -- if an item does not have a shipping method to a specified location, buyers in that location will not be able to see that item. This is often a problem for export sellers that do not ship to their own location.
On Vacation -- if you put your store on vacation, your items will be hidden from search. After ending a vacation it may take a day or two for your listings to be re-indexed and appear again.
In addition there are some known location-specific issues that affect particular users.
Each sponsored listings should show up both as a "sponsored" listing that will often have a higher sort position, and a non-sponsored "organic" listing that should sort correctly. The exception to this is if you use the "Best Match" sort; in that sort, only the highest sort version of the listing may appear. Note that if you use an ad blocker, you may be blocking "sponsored" listings, so do not use "Best Match" if you use an ad blocker and want to see all possible listings.
