For anyone else with this issue, I figured it out.

- Go to Service Portal -> Menus and click on the "Header Menu" that has the title of "SP Header Menu"

- Scroll down to the bottom on the next screen and click on the "Angular ng-templates" tab and click on "menuTemplate"

- You need to delete the 2 highlighted bits below in order to always show Requests/Approvals:

Easy...just had to find it.