An implacable person just can’t be appeased. If you really offended your best friend and tried every kind of apology but she refused to speak to you again, you could describe her as implacable.
Implacable is derived from the verb to placate, which means to soothe, or to appease. If you’re babysitting and the kid starts screaming the moment that his parents leave the house, and nothing you give him, be it a toy or ice cream, can calm him down, he might seem implacable. But try the TV. It tends to turn screaming kids into silent, happy zombies.