wesmorris:
Congratulations, you answered your own question.
In a true, perfect vacuum, the two bodies (the Sun and Earth) would orbit their common center of mass, following the exact same ellipses, forever -- without losing energy, velocity, or anything else.
The universe is, of course, not a perfect vacuum! The Sun emits light, some of which impinges upon the Earth's surface. The force is in opposition to the gravitational "pull" of the Sun, and tends to push it out to more distant orbits.
On the other hand, as has been mentioned, the Earth also encounters space junk all the time -- you could think of the Earth as bustling through a thin soup of space sludge. This material exerts what is effectively a drag force, and tends to slow the Earth down, which tends to push it toward closer orbits.
Physical problems are often fraught with this kind of stuff: we analyze the very simplest possible example of a phenomenon (two bodies moving in a total perfect vacuum) to extract the basic physical laws. To fully predict the Earth's real trajectory for billions and billions of years, however, is impossible. Passing comets, asteroids, perhaps even stars -- they'll all perturb the orbit and screw it up.
In general, astrophysicists consider orbits to be "chaotic," and thus are an example of a much wider field of problems. For any small piece of time centered around a known data point, you can pretty much predict exactly where the Earth will be. In the case of our own orbit, a billion years or so seems reasonable. Beyond that time, though, the errors begin to get pretty severe -- there are just too many variables, and they all accumulate and cause "feedback." We can say with pretty good confidence where the Earth will be in a hundred thousand years -- but we have little confidence that we know where it will be in four billion years.
Note as well that this is classical physics -- wherein energy states are continuous and forces can be any arbitrarily small magnitude. In quantum physics, things are more rigid -- you can often make predictions for a system that are valid for all of eternity!
- Warren