Branding isn't just a logo, it's a theme.

While the logo is a major component — arguably the most important one —, there are many other pieces that fit together to form a cohesive brand, such as the color scheme, typography, tone (e.g., serious, humorous, etc.), and other design elements.

You must have a logo that is bold and easy to process.

It does not matter how many times or places a logo seen, if it looks like myriads of other logos, or it's one that is overly embellished to the point that it becomes a blur, then it leads to vague familiarity. 

Vaguely familiar does not translate to trust.

The association game.

Think about the number of times you have seen a logo on the uniform of an athlete or along the edges of a football field. The sponsor will do this for two reasons: It understands that repetition often leads to a logo leaving an indelible impression in the minds of spectators, and seeing its logo on your favorite athlete will result in fans associating the brand with their hero. Both of which achieve the goal — being remembered and trusted.