So I've seen lots of successful writers use this technique. Someone already mentioned GRRM who used the technique more than once in the first book of his Song of Fire and Ice. One character is knocked out early in the battle. On another occasion, a character not involved in a battle merely recounts the experience of listening and worrying about her loved ones. Then people return and inform her of the battles results.
GRRM uses the technique less and less in subsequent books. I think that says a lot about the value of using significant omissions. Instead, he uses a cliffhanger at the end of a chapter, switches to different characters for a few chapters, then returns to the original character where the cliffhanger is resolved but then builds up some new tensions or suspense. It's a very powerful tool as you don't even notice that many of his cliffhangers end up not being real threats to the character. However, there are enough cliffhangers that are truly a cliff, so to speak, and thus the reader has trouble catching on. In the end, they aren't really significant omissions since what happened in between wasn't significant, but merely a way of maintaining suspense as long as possible.
Tolkien uses the technique once in the Hobbit when Mr. Baggins is knocked out during the final battle, a technique echoed by GRRM.
I believe the one hard and fast rule I can say for significant omissions is that you can't omit the climax. You just can't. GRRM doesn't do it. Tolkien maybe did it but that guy could do whatever he wanted.
In other works, the technique seems to be used mostly for battle. This is likely due to combat being difficult to write well, so most writers avoid it entirely. I admit that it's tempting. Prose is not the most effective medium for fast-moving, high-stakes scenes. But I still think we should try.
