I think 「お前は負けだ」 is not correct because it's incomplete as a Japanese sentence. The part 「お前は」 requires a verb, so you have to use an appropriate verb (in this case,「負けたんだ」. The part 「お前の」 means "your", so 「お前の負けだ」 is correct (It's your defeat." ) I hope the above explanation can help you:)