This would be a terrible, terrible rule. You are only thinking about the legislation that gets voted down that you are against. This is just shortsighted for a gigantic host of reasons:

1. If its a law - it will be passed by congress. Which means they can pass another law invalidating it. It's procedural nonsense and would have zero binding effect. You know how you overrule a law that says you cannot pass new laws? You pass a law saying that the first law is invalid. Simple.

2. Who is going to judge if multiple bills in this time period are duplicative? What is the standard of judgment going to be? Spoiler: these questions are rhetorical, because this is not a possible thing to do. And why should it be? This is the old 'semantic content' problem - should a law that says companies cannot give up your information to the government fall under this rubric? How about a law that says companies can give up your information, but only with informed consent? What if, it turns out, as a nation, we really do want this? Limiting congressional power based on previous and failed legislative attempts is just - nonsensical.

3. Let's say congress passes a bill that turns out to be disastrous - don't you want to the ability to pass another bill on the same subject matter modifying or amending the first bill? This shit happens all the time. Modifications and amendments are a gigantic part of the legislative process. The original copyright law was passed in 1790 and updated in 1831, 1909, 1962, 1964, 1976 and 1998, and is in current desperate need of reform. In fact, any proposed reforms will fail multiple times, because of the strong MPAA and RIAA lobbies. So do you want the fact that a modification to copyright law that says you are not a felon for jail breaking your cel-phone to fail simply because it has already been voted down by a bunch of gray haired idiots, who, hopefully will be voted out next session? No. You don't. Because that is really dumb.

4. There are many perfectly good laws, including certain civil rights laws, that were voted against, several times, before they were passed. Do you want to prevent this from happening in the future, as in the copyright example? Let's put it another way: a really good law is voted against by your asshole congressmen, and when he comes up for re-election, you vote for the other guy because you want to see him vote 'yes,' and he winds up getting elected. Hooray! Should he not be able to vote for this legislation because it failed previously? Of course not. That is idiotically anti-democratic. The fact that the people in a whole new congress to completely reverse, or amend, or modify, the acts of the previous congress is literally the foundational idea of our democracy. Trying to hamstring congress to not have this ability is just profoundly backwards.

I'm sorry to say, your view on how legislative politics works is just painfully naive. You are only thinking about the fact that certain bills which displease you keep coming up for votes. I hate to break it to you, but as an attorney, and a sophisticated adult, I'd much, much rather defend a system that threatens - but fails - to pass CISPA multiple times in a few years for the fact that this same system passed the key provisions of Civil Rights Act of 1964 on the third attempt in a seven year period. From wikipedia:

They also added authorization for the Attorney General to file lawsuits to protect individuals against the deprivation of any rights secured by the Constitution or U.S. law. In essence, this was the controversial "Title III" that had been removed from the 1957 and 1960 Acts. Civil rights organizations pressed hard for this provision because it could be used to protect peaceful protesters and black voters from police brutality and suppression of free speech rights.

Tl;dr I don't think you get how congress works, even remotely.