This is the thing that makes it seem impossible, it's easy to think that because it becomes akward the only solution is to end the friendship or allow it to just fade away.
It's fair to say that many of these relationships that develop while both people are adults will at some point experience sexual attraction, mutual or not, but it's no different than any other type of relationship problem, like if a marriage suffers a lack of sexual initmacy it isn't a reason to get divorced, it's seriosuly tough to get back to a good place, but people who make the effort do seem to make it back.
Having a close platonic friendship with a man/woman is doable, but like any serious relationship the people involved need to be aware at the start of likely problems they'll face and be prepared to rise to the challenge when it comes, not just pursue a friendhhip with their fingers crossed that their feelings won't evolve somewhere down the line.
After all it is a bit naive to think that if you like a person enough to want them in your life everyday that at some point it won't stray into romance, it can be dealt with, but only if both people truly value the friendship.