Suzanne B. Shu and Kurt A. Carlson have a paper (pdf) on this claim:
How many positive claims should be used to produce the most positive impression of a product or service? This article posits that in settings where consumers know that the message source has a persuasion motive, the optimal number of positive claims is three. More claims are better until the fourth claim, at which time consumers’ persuasion knowledge causes them to see all the claims with skepticism. The studies in this paper establish and explore this pattern, which is referred to as the charm of three. An initial experiment finds that impressions peak at three claims for sources with persuasion motives but not for sources without a persuasion motive. Experiment 2 finds that this occurs for attitudes and impressions, and that increases in skepticism after three claims explain the effect. Two final experiments examine the process by investigating how cognitive load and sequential claims impact the effect.
Here is a NYT summary of those results.