Ray,
The change is mainly due to the gravitational perturbations of the major planets. The orbital period is very sensitive to the eccentricity so a small change in e has a big effect on the period since a = q / (1 – e) and P = a^(3/2). The attached plots show the results you get if you integrate the current orbit forwards and backwards including the gravitational effects of all the planets and the biggest asteroids. There is a clear 12 year signature which is Jupiter but you can also see the large change in period corresponding to the small change in eccentricity.
