The simple rule is that "is" is present tense and "was" is past tense. If it's happening now, you use "is". If it happened in the past, you use "was".
But yes, you quickly run into problems like the example you cite. If you are describing someone's status in relation to a specific past event, that status will presumably exist forever.
If you said, "John is the tallest man in the room", that indicates he is the tallest man in the room RIGHT NOW. Of course "now" here means "at the time this statement was made. If I said this an hour ago, and then a taller man entered the room, you wouldn't say that my statement is false. It was true when I said it. But if a taller man enter the room, and THEN I say, "John is the tallest mean in the room", this is false. He was an hour ago, but he isn't now. If I said, "John was the tallest man in the room at 8:00", that statement would be true forever.
But when you are talking about a specific event that occurred at a specific time and place, a status associated with that event lasts forever. If I said, "John is the winner of the Tallest Man in the Room Contest of 2015", that is true forever. He was the winner of that contest in 2015. In 2016 or 2017 or 3017, he will still be the winner of the 2015 contest.
Still, once the event is past, we usually phrase it in the past tense. We don't say, "George Washington is the first president of the United States", because he isn't president any more. We say "George Washington WAS the first president."
In the case of "two-time nominee", that refers to a status the person has now, no matter how you look at it. She has been nominated twice. The two times may both be long ago, maybe she was nominated in 1962 and in 1973. But she still has the status of having been nominated two times.
It reminds me of the time a politician came to speak at my high school, and the principal introduced him as "a former graduate of Northport High School". When he got up to speak he said, "I thought I still was a graduate." For of course he was. He was a graduate the day they gave him his diploma, and he will remain a graduate the rest of his life.
Once someone dies, we usually refer to any status they had as past tense. When the two-time nominee dies, people will say, "She was a two-time nominee", not "She is ..." Likewise when I die, people will say "He was a graduate of Northport High School", not "he is ..." (Assuming anyone had any reason to talk about me at all!)