Those are pin terminals, and they're really awful. I'd remove all of them and install a set of five-way binding posts.
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Assuming there's good contact between the entire cable and the terminal (which presumably there is if the cable ends are soldered), you should be ok, soundwise. From your description, it doesn't sound like they are actually coming loose. But it wouldn't hurt to upgrade the terminals, either.
It's also possible that the soldering, by making the cable ends stiffer, is making it harder for the terminal to grasp the cable. Attach a piece of bare wire to a terminal, and see if the connection is firmer. If it is, snip the soldered ends off your cables and use bare wire.