Another question from my childhood:
A book, possible title being Star Kings, but nothing I can find under that title matches.
Alien race destroys all humanity, except one ship, a cruiser Challenger. The Challenger sends off multiple lifeboats with one (?) human plus germ banks in various directions, then is destroyed in hopeless battle.
Time passes. One genius in one of the few remaining lifeboats learns enough about the aliens to defeat them. Humanity re-arises and becomes the ruler of the Galaxy, possibly as the Star Kings, but become lax and are almost destroyed/wiped out overnight again. Slow recovery and...