CrashlyticsのMavenリポジトリから新しいFabricのリポジトリにした後、Gradleのビルドが信じられないほど遅くなりました。

この問題はGradleが依存関係を解決するうえで、FabricのMavenリポジトリが 401 Unauthorized を返しているので引き起こされているように見えます。

Failed to get resource: GET. [HTTP HTTP/1.1 401 Unauthorized: https://maven.fabric.io/repo/com/android/support/recyclerview-v7/maven-metadata.xml]
Failed to get resource: GET. [HTTP HTTP/1.1 401 Unauthorized: https://maven.fabric.io/repo/com/android/support/appcompat-v7/maven-metadata.xml]
Failed to get resource: GET. [HTTP HTTP/1.1 401 Unauthorized: https://maven.fabric.io/repo/com/android/support/support-v4/maven-metadata.xml]
Failed to get resource: GET. [HTTP HTTP/1.1 401 Unauthorized: https://maven.fabric.io/repo/com/google/android/gms/play-services/maven-metadata.xml]
Failed to get resource: GET. [HTTP HTTP/1.1 401 Unauthorized: https://maven.fabric.io/repo/com/android/support/support-annotations/21.0.2/support-annotations-21.0.2.pom]
Failed to get resource: GET. [HTTP HTTP/1.1 401 Unauthorized: https://maven.fabric.io/repo/com/android/support/mediarouter-v7/19.0.1/mediarouter-v7-19.0.1.pom]
Failed to get resource: GET. [HTTP HTTP/1.1 401 Unauthorized: https://maven.fabric.io/repo/com/android/support/support-annotations/maven-metadata.xml]
Failed to get resource: GET. [HTTP HTTP/1.1 401 Unauthorized: https://maven.fabric.io/repo/com/android/support/recyclerview-v7/maven-metadata.xml]
Failed to get resource: GET. [HTTP HTTP/1.1 401 Unauthorized: https://maven.fabric.io/repo/com/android/support/appcompat-v7/maven-metadata.xml]
Failed to get resource: GET. [HTTP HTTP/1.1 401 Unauthorized: https://maven.fabric.io/repo/com/android/support/support-v4/maven-metadata.xml]
Failed to get resource: GET. [HTTP HTTP/1.1 401 Unauthorized: https://maven.fabric.io/repo/com/google/android/gms/play-services/maven-metadata.xml]

古いCrashlyticsのMavenリポジトリは 401 Unauthorized を返してきません。

何か解決策はあるでしょうか。

これは、実際に私が遭遇した問題を解決できたStack Overflowの質問を翻訳し、編集したものです。
android - Fabric maven repo causes slow gradle builds - Stack Overflow