It depends on the AI file. Yours may be way too complex or have properties that are not compatible with video production. I have to admit that I am curious every time I see a post about converting vector layers to shape layers. In almost every case, converting to shape layers was an unnecessary step. There are only 3 reasons to ever convert a Vector layer to a shape layer.
You need to animate the bezier path in the original vector layer
You need to use Shape Layer animators like Trim Paths, Pucker and Bloat, Repeater or add something else from the add menu
You need to export a 3D comp to C4D or use the C4D rendering engine so you can extrude a vector layer
Here's what you lose when you export a vector layer.
Gradient fills become solid gray
Clipping masks fail
brushes don't turn into strokes, they turn into filled shapes
all AI effects fail
Unless you need to do one or more of the things in the first list, you are wasting your time.
Also, extremely complex AI files with hundreds or thousands of paths are not suitable for importing into AE as a comp. There are guidelines for preparing vector art for use in video production that should be followed. The closer your system is to the minimum system requirements the simpler an AI file needs to be used in a comp.
Maybe what happens is that your vector graphic is too complex, you should look at the number of layers and sublayers you have in Illustrator because this tool converts each one as an independent form, so if you have a very complex graphic you will have many sublayers inside the layers and this will make you get infinite shapes making After Effects collapse.