"available at that hour" is correct and usable in written English. You can use it when you want to refer to something that is accessible during a given time period. For example: "The store is not normally open on Sundays, but it is available at that hour for online orders."
A little after dawn, we awoke and set out again, and with more people available at that hour to ask for directions we did find the road.
The doctor treated him with 500 cubic centimeters (about a pint) of water, evidently because nothing else was available at that hour.
In all fourteen patients measurements were available at baseline, 1 hour, 2 hours and 4 hours.
Is child care that's available at all hours the "wave of the future," as one expert in the field suggested?
European filmmakers, not surprisingly, worry that their movies, already hard to export in their native languages, will be drowned out by films and shows that are available at all hours, at home, for little money, or at least a small fraction of the current €10, or $13.25, it costs for a ticket to a Paris movie theater.
That we all loved each other, that our homes were always open to each other, that we were available at all hours for brothers who needed us.
Dishes from all over the country are available at every hour of the day.
These orbits shall be available at 3 hour intervals with a latency of 2 hours after the actual observation for the application of GPS atmospheric limb sounding.
Whatever ethnic food you are in the mood for — it's all around the corner and available at any hour.
The mantra in many political campaigns, especially presidential, is "You can sleep after election day". Because of the 24-hour news cycle, staffers are expected to be available at any hour, even if it is three o'clock in the morning.
With no doctors in the country available to write a new script at that hour, and no money in his pockets, Baker says he felt forced to fend for himself over the weekend.
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union