base on my experience, so take it as an assumed estimation of your fellow groupsman .. It maybe accurate or not but im going to give it a try ..

Group Activity Refreshes every after the Saturday's Great Ninja War, so 5am of Sunday .. That's when the 3-Days Activity starts, Sunday 5am to Monday 5am (Day1), Monday 5am to Tuesday 5am (day2) and Tuesday 5am to Wednesday 5am (day3) .. It means, whatever you do after 5am Server Refresh on Wednesday, your 3-Day Activity will no longer increase for you to reach the required 200 points if your points is low since the next time it will record is at the next server refresh .. If you're group is lacking some numbers to reach the minimum requirement of 200 points, you must do it all on Tuesday ..

Now for the explanation you're looking about why does your points go up in morning to evening is simple, that's because your group members are doing missions and daily activities that adds the 3-day activity points .. and that usually happens every 3-days after the Saturday Great Ninja War, after that it will still increase but if you don't manage to get atleast 200 before the Wednesday refresh, then your chance to join in GNW will be gone ..

Edit : oops! i think i got dizzy on my own explanation when i read it the second time xD ..

no man, is my bad maybe I did explain poorly.
What i meant to say is:
I know that the system refreshes at 5AM every day, but it has happened to me, more than once that, in a Wednsday, at 10AM(server time) i had 194 activity, and then, at 17PM(server time), somehow, i had gotten 214 and thus I could join the war, again, this has happened to me more than once, when I almost lost hope over going to war, and there it was, a random refresh of the Group activity, that allowed me to go to war, anyone has any ideea how did that happen?

Group activity is 3 days worth. If you want into the gnw you need all your group members to do 6/6 group activity on Friday Saturday and Sunday. Then on Monday you will hopefully have 200 Group activity points. The rest of the week they can slack off with Group activity. Also if your group doesn't want to do stuff on Friday you can then do it on Saturday , Sunday, and Monday and then Sign up on Tuesday