My 3yr has really bad breath. The smell is still there after brushing. What is the cause and how can I help?

Various causes. Many people associate bad breath with bad hygiene, but commonly misdiagnosed or unchecked items are allergies, reflux, and airway obstructions. Use a team approach with the dentist, ENT and pediatrician.
More information. Does your child have allergies or a post nasal drip? There are many causes of bad breath, both dental and medical in origin. See the following website for more information and then if necessary have a consultation with a pedodontist and\or pediatrician as necessary.
Bad breath in Kids. Many children are mouth breathers (sleep with their mouths open). The mouth dries out and the saliva does not have an opportunity to wash the bacteria away that accumulate on the teeth, tongue and cheeks. Another cause might be digestive issues such as acid reflux which would be unusual in a young child, but first get a complete dental checkup and cleaning.