Which kind of contamination do you mean? Basically, any cell culture can be contaminated by an incorrect handling. Usually, it happens when you touch something not sterile with the tip of your pipette and than you use the same pipette to process cells. Contamination with molds is more common, since antibiotics added in the medium are generally sufficient to prevent bacteria contamination. If you use a medium without antibiotics you must be very careful since the risk of contamination is far higher
if is a bacterial contamination, the first thing I would do is to test another batch of cells, if it's possible. A contaminated batch is often the cause, especially if the contamination occurs quickly. I'd also suggest you to carefully clean your incubator, because sometimes it can depend on it.
I never observed bacteria contamination in stabilized cell lines, probably because they grow fast. I had contaminations in primary cultures when they couldn't grow well in plates. And, as I told you, when cells were non handled properly.