What file format are you using? Are you using collada or GLTF, or something else?
I have found for making imported animations loop, one of the only ways is to remove instancing through "make local" and then set the animation to loop. There might be a flag or something that you can select in Blender to tell Godot to make the animation loop, but I am unaware of it. Making the nodes local will remove instancing though, so reimporting the scene will not have an effect.
Another thing to try is making the children nodes editable, which is an option when you right click, but I personally have had hit and miss luck with changing the AnimationPlayer when the children nodes are editable.
All of that said, it is quite possible that I am missing something in my workflow. I've been using Collada with Blender 2.7 using the Better Collada plugin, but things may be different with newer versions of Blender and/or different file formats.
I would suggest putting something like "Godot <File Format Here> import workflow" in the search engine of your choice and see if that pulls up some results tailored for the file format you are using.
