To anyone's knowledge, has there ever been an object that approached the earth and was captured into an orbit? Is it thought that there might be such objects simply too small to spot or just not discovered yet?
I may not qualify as more knowledgable but here's what I can add to @called2voyage's comment.
In the question Have there been any documented mini-moons since 2006 RH120? I link to Granvik, Vaubaillon and Jedicke 2012 (The population of natural Earth satellites Icarus, 218 (1) March 2012, pp262-277) available without paywall in ArXiv.
We have for the first time calculated the population characteristics of the Earth’s irregular natural satellites (NES) that are temporarily captured from the near-Earth-object (NEO) population. The steady-state NES size-frequency and residence-time distributions were determined under the dynamical influence of all the massive bodies in the solar system (but mainly the Sun, Earth, and Moon) for NEOs of negligible mass. To this end, we compute the NES capture probability from the NEO population as a function of the latter’s heliocentric orbital elements and combine those results with the current best estimates for the NEO size-frequency and orbital distribution. At any given time there should be at least one NES of 1-meter diameter orbiting the Earth. The average temporarily-captured orbiter (TCO; an object that makes at least one revolution around the Earth in a co-rotating coordinate system) completes (2.88 ± 0.82) rev around the Earth during a capture event that lasts (286± 18) d. We find a small preference for capture events starting in either January or July. Our results are consistent with the single known natural TCO, 2006 RH120, a few meter diameter object that was captured for about a year starting in June 2006. We estimate that about 0.1% of all meteors impacting the Earth were TCOs.
The paper describes an exploratory simulation of the probability of objects being captured into at least temporary 3-body orbits in the Earth-Moon system, also taking into account perturbations from the Sun. Usually the orbits last a few months. Longer orbits are less common.
There is certainly the small possibility that an object could spend several years or longer, but the probability of this naturally decreases as the the lifetime increases. You can think of it as the "keyhole" for entering a long term 3-body orbit shrinking as the duration of that orbit increases.
The population of near Earth objects to be captured decreases as the size increases. Thus there could be many temporarily captured objects of micrometeor size, but few large enough to be easily observed. The chaotic nature of these loosely-bound orbits makes them harder to track and analyze; you can't assign Keplerian orbital elements and look for repeat passes.
What is really surprising is the first sentence of the conclusion (Section 4):
We provide the first estimate of the orbit and size-distribution for temporarily captured natural irregular satellites of the Earth. We predict that there is a one-meter-diameter or larger NEO temporarily orbiting the Earth at any given time.
You can also listen to the conference call with Bill Bottke (MP3 plus other documents) about "minimoons" presents an alternative to Asteroid Redirect first got me interested in orbital mechanics.