How long do Bloodhound's clues stay visible?
Solution 1:
When looking at clues, you will notice they have a timer that counts up. This timer counts up to 60 seconds. Thus clues only remain for 60 seconds. Additionally, the clue icons have an animation around the border of them that also indicate how old the clue is.
Another source that indicates this:
Tracks left behind by enemy players only last 60 seconds