I didn't test it but based on the tooltip I would say:

- Every time you deal direct damage you gain a stack of resolve.
- You can only earn one stack of resolve every 0.5 seconds.
- Each stack of resolve stays active for a maximum of 5 seconds.
- The maximum amount of stacks is 9.

Thus, I would say that each individual stack has a five-second cooldown.
If a stack of resolve runs out (after 5 seconds) you can immediately get a new stack for five seconds unless you just gained a stack of resolve <0.5 seconds ago or you are already at the maximum amount of stacks (9).

So:
When you deal direct damage and gain one stack of resolve for 5 seconds, after 5 seconds this stack runs out.
If you deal direct damage >0.5 seconds after gaining your first stack of resolve, you gain another stack of resolve with a 5 seconds cooldown. And so forth, until you reach 9 stacks. Suppose you reached the maximum amount of stacks and 5 seconds have passed since the first time you dealt direct damage and gained your first stack, you simply lose this stack and can gain a new stack of resolve by dealing direct damage (unless you just gained a stack of resolve <0.5 seconds ago)