All your sentences are correct. You are using the present participle as a noun, and this is something you are allowed to do. It may not always be the best choice, though. I would say
"They can't stand that they fail to measure up to her"
"They can't stand that they fail to rival her"
"They can't stand that they fail to be her equal. "
I like the last two sentences as they are.
The reason I prefer "that they fail" is that it is precise. It pinpoints the thing they cannot stand. "Failing" in the other hand only creates an image. It is less precise. If you can't stand something, you want to be precise about what it is that you cannot stand.
The last two sentences are different. "Not sitting well" and "not going over well" are much less intense than "cannot stand". There is less need for precision. An image is sufficient, so the present participle "selling" works well.