Is there an issue with the war energy not being replaced after one round of fighting?
What do you mean exactly?
You get 3 war flags in the beginning of the war. Then you get an additional 3 flags at 12 hours mark regardless if you attacked or not.
This is for all alliance members.
Hope this helps
If you go to the battlefield, there should be a little timer in the top left I think that shows when your flags replenish.
But as said, you only get six, in two lots of three, over 24 hours
War energy is only refilled once at exactly 12 hours after war begins.