My grandmother was diagnosed with Stage 4 Pancreatic Cancer in March of this year, and passed away in April. I was extremely close to her, so her illness and death were extremely hard on me. I am not a religious person, but she was, so I spent countless hours praying that she would be cured and lost even more faith/hope as she progressively got worse. 

Since her death, I have had nightmares of her dying of cancer over and over again. In each dream she is extremely sick and in the process of dying, but the scenario is always different. Last night I had a dream that she was sick and dying, as I normally do, but I was super upset because I had not gotten a chance to say goodbye to her. I spent the dream trying to get to her house before she passed away, and finally made it to her and laid down next to her and gave her a hug. While that doesn't sound too awful when I type it out, it is extremely stressful to keep having these dreams and they do not always have "good" endings. Are these dreams a sign that something bad is going to happen to me? Is it punishment for losing my (already minuscule) faith in God?

You've lost someone who gave you unconditional love and that may be what is 'haunting' you. Not having it and in dire need of it. The underlying reasons for that developed attitude goes back to early life. Unconditional love in childhood is as essential as breathing. Being a wise old women your grandmother may represent more than unconditional love, she may trying to tell you to learn to love yourself, those aspects that were essential but lacking in early life.