The problem may occur in following condition:
While Uploading GIF image in post/pages
While Uploading GIF image in widget

While Uploading GIF in post/pages
When you upload your GIF in WordPress, Go to the image settings of the GIF and under the image size option, select Full Size. You can see image below:

Notice the red box at the bottom right of the editor. This is where you select the image size. Be sure to choose Full Size. While choosing full size WordPress uses the original image that you uploaded.

Uploading GIF in Widget
When you add your GIF from Media, go to the attachment display settings at right bottom and Select Full Size from Size. You can see image below.

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