In general, to invest means to allocate something in the expectation that one will benefit something in the future. Personal relationships, on the other hand, is the kind of connection you build with people through emotional bonds and interactions.
Now, to say that one is not investing too much, in my opinion, means that you are not putting yourself out there to the point where people will really get to know you. For some reason or another, you do not expose yourself too much such that people won't discover the real you. On the other hand, this may also mean that you are interacting with people but you are only building shallow connections that won't really matter whether or not it will last.