Quality index is the overall quality of your ad across all the keywords for which it shows. When you have multiple keywords in your ad group, your ad might perform better on some of the keywords than others. Therefore, a high quality index could still mean that although your ad is performing well overall on most keywords in the ad group, it’s possible that it’s not performing well on the others, which will prevent your ad from displaying when searching for those particular keywords.
We recommend that you structure your ad group so that all of your keywords are as relevant as possible to the ads in the same ad group.