Because they are more highly focused, they have less reach, which many do not consider a drawback. You must submit your final copy and ad prep many months before deadline. Some magazines have a fast close, and other will call up repeat advertisers with last minute deals, often because they have space to fill or when others back out at the last minute. Although once they start printing, you cannot backout. Generally, once you buy a magazine ad, you are locked in no matter what.
Refunds are rare.
You do not get high frequency unless you buy an entire year's worth, but then readers will see them about once a month for most magazines. You get superior quality color on high quality paper, allowing for effective product presentation, if you are willing to pay top dollar. Many people live to scan and clip coupons. You get ample opportunity for long copy. Sunday magazines are among the best place to make a long, detailed ptich.