Not an expert, but as long as it isn't an clone using the same DNA. There will always be a chance for mutations. Their offspring are near, but not exact. Whatever happens they are gaining males with a Y.

Now if you are thinking of diseases like human inbreeding does. All species do have that problem. They just die off or it's a common problem with XYZ. Humans live longer than their breeding age and they are many, many people. So problematic mutations just stick around and get worse.