There were very few members of the Order that could have been called for such a duty in the "Order of the Phoenix" at that time and the Order was probably talking of their plans and deciding how they should go about guarding the Ministry. Because their ranks were very low.
Also, Dumbledore might have decided to give up protecting the prophecy as it was not worth it and due to their ranks being very small, almost impossible.
No one was there, because:
- They were regrouping
- They didn't expect a surprise attack
- They were low on trusted personnel
- They didn't expect trouble
Everyone during the events acted like they were sorta calm. That leads me to believe that everybody was calm, because they had no idea of what was going on. They must have thought that the Ministry was safe during that time, possibly due to something Snape or someone heard, but nevertheless everybody seemed calm.
"When, however, you did not return from your trip into the forest with Dolores Umbridge, Professor Snape grew worried that you still believed Sirius to be a captive of Lord Voldemort's.
Meaning he wasn't worried before.
"Alastor Mood, Nymphadora Tonks, Kinglsley Shacklebolt, and Remus Lupin were all at headquarters when he made contact...
And they certainly didn't seem that worried. They were at the headquarters instead of guarding.
The ministry was in the between times for a member of the Order to go check on it. And that is why no one was there, because they didn't get there in time to cover for the others. They had few members so the ones that were taking shifts didn't have enough time, between other duties, and so there were gaps between shifts. And that is why no one was there.
They were low on personnel
Well from taking a tally of all of the "Order" members it says that they were all elsewhere or incapacitated.
And Harry thinks explicitly that there is no one that he can call to help him.
pg.730, Chapter 32, Out of the Fire
There was nobody left to tell. Dumbledore had gone, Hagrid had gone,
but he had always expected Professor McGonagall to be there,
irascible and inflexible, perhaps, but always dependably, solidly
Professor McGonagall — laid up in a hospital wing.
pg.730, Chapter 32, Out of the Fire
"I need to see Professor McGonagall," gasped Harry, the breath
tearing his lungs. "Now... It's urgent...."
"She's not here, Potter," said Madame Pomfrey sadly. "She was
transferred to St. Mungo's this morning. Four Stunning spells straight
to the chest at her age? It's a wonder they didn't kill her."
Molly Weasley — at home or with Arthur
Arthur Weasley — convalescent
Dumbledore and Hagrid — gone:
pg.723, Chapter 31, O.WL.S
"At least they didn't get to take Hagrid off to Azkaban," said Ron.
I'spect he's gone to join Dumbledore, hasn't he?"
"I suppose so, said Hermione, who looked tearful. "Oh, this is awful,
I really thought Dumbledore would be back before long, but now we've
lost Hagrid too..."
Because remember Dumbledore went into hiding in "Order of the Phoenix".
Snape — At the school. Doing professor duties or whatever.
Then on pg. 830, Chapter 37, The Lost Prophecy
"Kreacher told me last night," said Dumbledore. "You see, when you
gave Professor Snape that cryptic warning, he realized that you had
had a vision of Sirius trapped in the bowels of the department of
Mysteries. He, like you, attempted to contact Sirius at once. I should
explain that members of the Order of the Phoenix have more reliable
methods of communicating than the fire in Dolores Umbridge's office.
Professor Snape found that Sirius was alive and safe in Grimmauld
"When, however, you did not return from your trip into the forest with
Dolores Umbridge, Profesor Snape grew worried that you still believed
Sirius to be a captive of Lord Voldemort's. He alerted certain order
members at once."
Dumbledore heaved a heavy sigh and then said, "Alastor Moody,
Nymphadora Tonks, Kinglsley Shacklebolt, and Remus Lupin were all at
headquarters when he made contact...
You could think this
Why didn't someone else come? There had to have been more members.
Because maybe the Order only trusted a few people for that particular job. And they wanted to make sure that the job was done right and it might have done more harm than good to allow someone who works with Voldemort to work for them.
Also, the Ministry might have not allowed them to protect the prophecy.
Among their goals was to obtain a record of the prophecy concerning
Voldemort and Harry, which was kept in the Department of Mysteries.
The Order kept guard on the area, but were hampered by the
Ministry's lack of cooperation.