Right - sorry. Let me try again.
I'm editing my sequence in Premiere Pro. It's done, but when I play it back, there's a black frame after my end card. I can't get rid of it, and I'm afraid that when I render the video, that black frame will be the last thing people see when they view it. Does that make sense?
The black frame you're seeing is not what will be the "last frame" of the video. Export and give it a try so you see what it will look like.
But no, you can't control what various players will do with the last frame of your video.
To "fake" the effect you want, add 10 seconds of your card at the end.