This happens if the rules Memo is required for time entry and Memo is required for expense entry are set for a project. With the right security permissions, you need to remove these rules from the Projects > Settings > Assignment screen if you want the time and expense entries to be saved without having to write a memo.
Note: If you un-check the rules Time/Expense entry memo required in Settings > Time & Expenses, they do not affect your existing projects and only apply to the new projects you create. So, you should make sure the rules are removed at the project level, as that takes precedence.