This is a fun question. The reasons why an Earth-like planet could go unnoticed for so long generates some interesting ideas.
In our own solar system, the main reason we discovered the non-classical planets (the classical planets being Mercury, Venus, Mars, Jupiter, and Saturn), is because we were actively looking for things in the night sky. (This is especially true for Neptune and Pluto.)
It's important to realize that things do slip through the cracks, in that some observation was misidentified, and it took a while to realize the mistake. This happened with Uranus, in that Uranus was seen by the ancients, but not recognized as a planet until until 1781. Pluto also has a history of having misconceptions: In 1931, Pluto was thought to be as massive as Earth; finally, in 1978 it was shown to be only 0.2% as massive of Earth. And from the mid-1800s to the mid-1900s, we assumed that our sister planet, Venus, could likely harbor life with an Earth-like environment.
We assumed Uranus was a star, when it was actually a planet. We assumed Pluto was Earth's rival, mass-wise. And we guessed that Venus could easily support life.
We didn't make these assumptions because we were stupid; we were just going with what we knew, based on the other things we knew at the time. And our assumptions occasionally cause us to incorrectly think about certain things for a long time, until we finally discover more of the truth.
We often speak badly about assuming things, but when you have so much information to process, and so little knowledge to go off of, sometimes you don't have much choice but to make certain assumptions. (And, believe it or not, often assumptions can be pretty accurate.)
That's why I say that it's pretty reasonable that certain things can "slip through the cracks." For instance, a solar system could have many, many planets that orbit in a exceptionally flat and circular plane. Therefore, it would be easy to miss a planet that circles its sun nearly perpendicularly. If you're only looking at the ecliptic for planets, why would you look elsewhere? That might not make sense to you or anyone else -- but that doesn't mean that there can't be a planet outside of the ecliptic plane.
It's not easy to find planets from one snapshot of the night sky, so a common technique is to take several photographs over a period of several days/weeks/months/years, and try to find points of light that move predictably, independently of the stars in the sky. But there may be literally billions of objects that move. How can you identify whether one is a sizeable planet, or just a relative speck of dust?
Often, these points of light are identified as asteroids, comets, or a Trans-Neptunian object. And since there are so many, you can't spend a lot of time investigating every single one, making it easy to assume that a cluster of moving points is just a cluster of rocks in an asteroid field.
Conceivably, your planet could have been previously seen off the ecliptic of planets, but since it was surrounded (or in the path of) asteroids, it was just dismissed to be tracked as "just another asteroid." When, in the future, it is noticed again by a younger astronomer, he/she would look it up in the archives, learn that it was classified as an asteroid, and then move on and forget about it.
It would take several of these sightings, and a realization that this asteroid is being noticed more frequently, before a theory develops that something is different about this asteroid, making it deserving of a closer look.
Just like Neptune, Pluto, and Venus, something was misidentified, and it takes a while to discover the mistake after we dismiss this important planet as an asteroid. There could be many reasons for this dismissal/assumption, such as:
- In a solar system of so many gas giants, it is unlikely an Earth-like planet could exist.
- We've scoured the ecliptic plane, and we're 99.99% sure there are no planets we haven't already found.
- If there were any other planets out there, we'd surely have found them by now.
Regardless of how invalid these reasons are, they're still reasons, and they all work against discovering any new planets.