There are lots of painted pools in our area and I take them on without question. If the paint is bubbled or clouding a lot when you brush it, it's on the down side of it's life and you should make that known to the customer before you take on the pool.
While there are lots of paint-over-plaster jobs around here, we have just as many paint-on-gunite pools (pools that were painted right from the start). Those are usually done with a chlorinated-rubber paint and can last a long time. I have one that's only now at the end of it's life after running for 12 years. The first ten were on biguanide, so it had a pretty easy life for a while, but impressive nonetheless.
Since they're the fastest to degrade (vs. plaster, vinyl or fiberglass) they're also the most prone to problems caused by poor water balance so keep that in mind.
As for the client you originally posted about, it sounds like that finish is done. Any idea how old it is? I wouldn't recommend leaving it as is. That will just make you and the customer both unhappy. If the customer doesn't already have someone in mind, call around and try to find someone who could take the job without taking the customer. Kind of an awkward situation to be stuck in, but like I said, neither of you will be happy leaving it as is.