At the point that the investor can't or doesn't want to handle it themselves anymore that is different for different people.
It depends on your goals
If you get to the point where you feel like you are a book keeper and no longer an investor, then get a book keeper.
If you get to that point and you are okay with being a book keeper because you have enough of what you want, then keep doing the books yourself.
I don't think there is a point. Some investors never hire a bookkeeper and do just fine using technology. Others hire a bookkeeper from day one because either they really hate bookkeeping or they figure out (correctly) that they could use their time better doing something more productive.
I really depends on you. I love bookkeeping so I enjoy spending the time doing it. If the thought of bookkeeping makes you want to tear your head off, its time you get a bookkeeper! Good luck!