Here's the article from a very reputable breeder:
Maltese and Eyestain
Eye staining is one of the most commonly discussed topics among Maltese owners and exhibitors. If you purchase books on the Maltese or ask Maltese breeders about it, you will find that the one thing that the majority agrees upon is that some dogs are more prone to staining than others and that there is no known cause or real solution to the problem.
The one thing that you can do to prevent the stain is to first control any excessive tearing before it gets out of hand. Eye infections, blocked tear ducts, allergies, teething, and ear infections including mites can cause excessive tearing. Make an appointment with a Vet and have them check for the any of these things. Ask them about antibiotics as a short-term way to control the staining. Another dynamic that plays a part in the staining is the environment that the dog lives in. You should keep your dog in a setting free from cigarette smoke, strong fumes from household cleaners, dust, and stress.
Get into the habit of cleaning the debris away from the corners of your dogs’ eyes every day starting the day you take your puppy home. You can use a 'soft' toothbrush or a comb with small teeth. Make sure that there are no small hairs poking into the eyes. This can cause constant irritation and eventually lead to infections. Cut any hairs that point directly into the eyes or have your Groomer do it for you. If the staining is an issue for you, before you buy a puppy, ask to see the parents. Many breeders think that the staining might be hereditary. Chances are that if the parents have the staining, the puppy will too.
Manny Comitini