Why can't I change that shift?

Most often, the shift is on a day that has passed, or it is a published shift you deleted, which waits as a cancellation. The reasons, most likely first:

1. Its day has passed. The message is That day has passed, so its shifts can't be changed. Days before today are locked, and their menus offer only Copy and Edit details. See Why are days that have passed locked on the roster?
2. It is a cancellation waiting to be published. It is greyed and struck through, and says Cancelled: press Publish to send. Its only menu choice is Keep this shift. Keep it to change it, or publish to send the cancellation. See Cancel a shift, or discard changes.
3. You cannot run the roster. Changing shifts needs the permission to run the bar and events roster, which the Bar Manager and Administrator hold by default. Without it, Weekly roster is not in your menu.
4. It is part of a slot. Pressing a slot picks it rather than opening a panel. Double-click it, or choose Edit details from its menu, to change the slot; changes to its day or times move every place on it. Choose Edit details on a person's chip to change only their shift.

Shifts for a function can be changed like any other on the roster. The function changes only its own date, times, name and the number of people it needs. See The function's staff on the roster.