Having a visible reminder of the minutes ticking away might spur you into speeding up your morning routine, rather than letting the time creep up on you.
Tiredness can easily creep up on you while you're driving.
Don't let poverty creep up on you and drag you down.
A bad habit can creep up on you if you don't monitor your behavior.
I would guess that modern humans, with no natural predators but themselves, and with all their toys and mental constructs and cosy rooms, are relatively easy to creep up on.
The hypothetical boiled frog is a useful metaphor for a very real problem: the difficulty of responding to disasters that creep up on you a bit at a time.
Love seems to creep up on you.
Anorexia can creep up on young girls when they least expect it.
The desire to be a mother may creep up on you unexpectedly.