Ancient thread, I know, but my wife's iMac has had this annoyance for years. iMovie only since iPhoto is no longer a thing.
Has anyone ever found the solution? No one I've talked to at Apple seems to have heard of it (does anyone there know how to Google?).
I'm on her machine right now. Have logged in and Accepted again — as I do 2–3x per year.
iMovie fires up and is at v. 10.1.11 — Wiki says the latest version is 10.1.10 so I know it's been updating and there's no real problem.
Still, it's things like this that annoy me.
[doublepost=1556994570][/doublepost]Hmmm... I may have found the solution. I deleted iMovie and tried to Install from the Purchased list in the App Store — no go because it won't Accept. Ok, I expected that.
So, I went back 10 minutes in Time Machine and restored iMovie — took about a minute (love APFS Snapshots!). Closed the App Store and reopened. The Accept box is gone. ??? Ok, that's good...
So, pushing my luck, I trashed iMovie again, closed and reopened the App Store again. The Accept button is gone and when I clicked on Install, it downloaded and installed like it was supposed to.
I'm declaring victory. Hope this helps someone else.