If your AI file does not have any raster effects like drop shadows and blurs, and you collapse transformations if you scale, there is no bug or problem with the image losing quality. The image should look exactly the same as it does in Illustrator if you turn on Pixel Preview in AI and magnify the comp panel in AE because the composition panel is pixels and not vectors.
The most common complaint from new users about AI files is that that they expect to be able to magnify the comp panel to 400% or more and still see perfect curves. When you look at the comp panel as 400% you have enlarged the pixels 400% so you can get a good look in exactly the same as enlarging the panel in Photoshop gives you a better look at the pixels in an image.
If you still can't figure it out, embed some screenshots that show the modified properties of your layer and the entire UI. It also helps if you have the AI file selected in the Project panel so we can see the properties. Show modified properties by selecting the layer and pressing the 'u' key twice.
* The "Drag & Drop here..." area is buggy and should not be used to share images. Please use the toolbar or just drag your images to the reply field.