I agree with a lot of what's been said, esp Joseph. So if you'll pardon me poking my FTM head in this thread...
...I had a similar situation with one of my best friends who has known me since I was 10 years old. She just kept butchering name and esp pronouns in public at first.
What I found helpful was having a serious conversation about how no one wakes up one day magically using the right pronouns (or name), just as no one wakes up one day fully transitioned with everything taken care of (clothing, voice, hair, let alone hormones or other medical stuff!). If she is waiting to just "get it right" at some point, that's not going to happen. There is no special pronoun/name fairy that will visit her, just like there is no MTF fairy that will visit you overnight, just like no one learns a new language by hoping they could speak it.
She has to TRY to use the right pronoun and name and she has to REMEMBER to keep TRYING at first. That's what you need to ask of her in a calm, but serious, manner. Recognize and tell her that it is hard for her, and you KNOW it is hard. But makes sure she understands that you have to "TRY" everyday is various ways to be seen as who you are, and it IS hard. It's hard for you, it's hard for her, it's hard for everyone. The way I phrased it in the early going is, "If I spend so much of my time and energy getting people to see who I really am on the inside, could you respect me enough to *try* to do these things that both respect who I am AND protect my safety? You can let her know that it is common to slip up and you are not asking for perfection. All you are asking for is an effort, and that your friendship - and safety - really depends on that effort.
The other part that I think is important to get to - after the trying - is the safety. I think we try to sugarcoat being trans for the people closest to us. We don't want them to worry and when we can be seen as we truly are, we ARE happier than ever. There is a disconnect with just how much discrimination and how dangerous it can be, and I think we all downplay that latter part to not worry our family and friends, wihch leads them to not take things about safety as seriously as they should. I think it's reasonable to point out that she is inadvertently jeopardizing your safety, and you would hate to have to choose not to spend time with her, because of your wholly rational fears about your health.