My dentist did a very poor job on my veneers and wasn't willing to replace them for me, is it reasonable to ask for a refund?

It may be your fault, but it
should have been diagnosed as part of your treatment plan when your veneers
were placed. If you are doing something that is out of the dentist’s
control like biting your finger nails or chewing on hard objects, then I would
consider you responsible. If however, you are chipping the veneers
because of the way your teeth come together or during normal function, I would
consider that your dentists should be the responsible party and either redesign
how your teeth come together when you bite or chew or recommend a night guard
to protect your new veneers. Immediate chipping of veneers is something that we
rarely see when they are placed properly and the occlusion (the way your teeth
hit and come together) is addressed properly

It can happen that they can chip initially and then can be smoothed out. However,if you're are not happy with results, then they should be redone at no charge. The dentist should have been aware before starting of areas that may be issue due to habits. I would call or write the office and let them know of your dissatisfaction. 

We have a fool proof method that will you will have a hard time getting a smile that you are not happy with.  We use a template, called a "trial smile" that is placed in for temporary veneers while the lab fabricates your new smile.  You can tweak the trial smile to a more idealistic end result and this communication is sent to our lab.  When the new veneers are finished, we always try them on first and allow the patient to preview them for as long as they like.  If they are not what you want, we would never place them in permanently.  Good luck!  Dr. David Frey