Employees are unable to view some projects in the Time Entries screen.
This can happen if the projects have a status other than Active. Only active projects and items display in screens and lists. So you need to change their status to Active before they are visible in the Time Entries screen. Check out this article for details on how to do that: Making inactive projects active.
This can also happen if you are using Project Assignments or Employee Control. If there are team members assigned to the projects, you should make sure to include and assign all employees that should be working on them. Only the team members assigned to the projects can make time entries on them. Check the Core Help for details. Similarly, if you are using Employee Control for the employees in the Time Entries screen, make sure that the projects they should be working on are assigned to them. By default, Employee Control will take precedence over Project Assignments if you are using both, unless you specify otherwise using security permissions. Check the Core Help for details.
Another scenario in which this can happen is if the rule Prevent time entry for the project is set for the projects. The projects are no longer visible in the drop-downs of Time Entries screen if this rule is set for them.