Why did Egyptians seem so preoccupied with continuity and permanence?

I don't believe that people are all that different over time. They think many of the same thoughts and feel similar feelings. To most people, the most important thing is self-preservation. So, it's only natural to try and leave a lasting impression or mark of themselves that will stay on after they've gone. Many people are survived by their children or family, and they are remembered that way.

To most, it's a scary thought we won't exist after we stop living. This is the one of the main reasons for religion: Where will we go when we die? It is also an attempt to answer where we came from, and as such, there are many creation stories all over the world.

In Egypt, it is important to know that the kings were viewed as heaven-sent, or God-Kings. They were intensely preoccupied with putting down images of their gods in stone and paintings, so it's natural that they would feel the need to preserve traces of their god-kings. This was ever more so important because these were gods in the flesh, rather than the ones told of in stories.

I think their was also a competitive air about the kings. They wanted to prove they were the greatest before their predecessors, and so tried to out-build them, be wealthier and have their images carved down for the future to see. They also believed that they would be able to take their wealth and status into the afterlife.

Above all else, I think Egyptians valued their history and felt a need to be recorded in ways which would not allow it to be forgotten.