Use 'all hours' to show flexibility or openness in someone's schedule or availability. The helpline is available at all hours for your convenience.
Pro Tip 2/3
Exaggeration Caution
'All hours' can sound like an exaggeration, so use it to emphasize extremeness rather than literal accuracy. I seem to bump into him at all hours—whenever I go out.
Pro Tip 3/3
Negative Connotation
Sometimes implies inconvenience or the excessive nature of an activity or situation. She calls me at all hours with trivial questions.