From the "Saving Projects" section of the DaVinci Resolve 14 Reference Manual (page 57):
As you work on your project, the word “Edited” appears to the right of the project name at the top of the DaVinci Resolve UI to let you know that you have unsaved changes. If you don’t save in over 15 minutes, the word “Edited” turns yellow, and if you still don’t save in over 30 minutes, it turns red to let you know that you probably should save. If you move the pointer over the word “Edited,” a tooltip appears letting you know when the last save was performed.