Some products are often bought as gifts. In this case, the demographic for the buyers can be quite different to the demographic who are interested in the site.
It can be quite difficult to use search to target these people; they don't know a lot about the type of product they are buying so the search volume tends to cluster around a smaller number of competitive head terms.
Here is a quick idea for targeting the people buying the gifts:
The idea here is to reach the computer used by the receiver of the gift whilst it is in use by the purchaser of the gift. The receiver browses sites in the relevant niche so Google identifies the browser as belonging to someone with that interest. Then when the gift buyer is browsing sites that interest them then they will see your ads.