You know that there is an approved BOB repair product designed to repair loose rear view mirrors.

http://www.octanecreative.com/ducttape/bodyshop/

It is a little over half way down the page.

Locktite is not recommended for use on plastics, at the bottom of the page on the right.

http://www.loctiteproducts.com/p/10/25/t_lkr_green/overview/Loctite-Threadlocker-Green-290.htm

The green locktite is designed to capillary into an already assembled joint.

If you don't need to move it again, drill a small hole all the way through the joint and install a bolt in it. Don't tighten the bolt to much so as not to crack the plastic. Have seen that type of joint loosen up before and i have not seen a good repair to fix it. Good luck and let us know what you do.