Since gravitational acceleration is a vector, we can sum the attractions from the sun and Neptune on Uranus into a single acceleration. We can then break that single acceleration down into two components: one towards the sun, As, and the other in the direction of motion, At.
We will now consider the orbits of Uranus and Neptune around the sun, and we will consider motion relative to Uranus. As Uranus catches up to Neptune, there will be a time where Neptune is straight ahead, and the angle sun-Uranus-Neptune is 90 degrees. Call that point QE (eastern quadrature). Later, Neptune will pass directly opposite the sun, as seen from Uranus. Call that point O (opposition). Later, Neptune will be directly behind Uranus, with the angle sun-Uranus-Neptune again 90 degrees. Call that point QW (western quadrature). After a long time, Neptune will keep being left behind until it is directly behind the sun as seen from Uranus. Call that point C (conjunction).
Now consider At. As Neptune goes from C to QE to O, At is always in the direction of motion of Uranus, and reaches a maximum between QE and O. As Neptune goes from O to QW to C, At is always against the direction of motion of Uranus, but with the same magnitude as it had going from C to QE to O. Hence Uranus will be accelerated for half the time and deccelerated half the time due to At, and the net acceleration will be close to zero.
Now, consider As. While Neptune goes from QE to O to QW, As will be decreased, causing Uranus to move further away from the sun. While Neptune goes from QW to C to QE, As will be increased, pulling Uranus towards the sun. Of course, the magnitude of this increase will be a lot less then the earlier decrease, because Neptune is much further away, but it acts for a much longer time! So again, the net result is to put Uranus back where it had been originally.
In summary, the effects of Neptune on Uranus can be easily detected for parts of the orbit, but the net result after a whole orbit is very close to zero. As Pearsonartphoto pointed out, the net result is not exactly zero because of second order and higher terms. But so far, celestial mechanicians have found that, while these higher order terms can cause periodic effects lasting tens to thousands to hundreds of thousands of years, all such effects seem periodic over the long term. After billions of years, chaotic forces dominate anyway.