This is just a guess, and maybe someone with access to the data can check this, but here's what I think happened: during the 60s, Southern whites started voting for Republican presidents while continuing to vote for local Democratic congressmen. After 1972, though, as the Republican shift of the South continued, they started voting for Republican congressmen too. In other words, I'll bet that the split-ticket phenomenon — both up and down — is almost entirely explained by the South, not by some massive nationwide shift toward independence.
I ran the numbers (they're in the chart below) and Kevin's partly right. Split-ticket voting has almost always been higher in the South (1964 is the exception). Nonetheless, both regions have seen a general decline in split-ticket voting over the last few decades.
The key point is that regardless of region, there's no evidence (contrary to what Mark Penn claims) of significant growth in split-ticket voting in recent elections.