[SDPhantom]

When dealing with StaticPopupFrame, it's best to hook into the event that calls it so it'll reliably run AFTER the code that shows the popup. In this case, UIParent processes the event, so that's the frame we want to hook.

UIParent:HookScript("OnEvent",function(self,event,...)
    if event=="PARTY_INVITE_REQUEST" then
        ShowFriends()-- Update friends list
        for i=1,GetNumFriends() do
            if (GetFriendInfo(i))==(...) then
                AcceptGroup();--        Accept invite
                StaticPopup_Hide("PARTY_INVITE",(...));--   Hide popup
                break;--    Stop scanning (we're done here)
            end
        end
    end
end);

Note: the only extra arg passed to the function is the name of the player inviting you. This is initially passed to StaticPopup_Show(), which assigns it as the popup's ID. You'll need to pass it to StaticPopup_Hide() hide the frame.