Why didn't the Ministry of Magic station a number of Aurors to protect the Potter family from Voldemort when the Potters were attacked on 31st July?

Because a bunch of people in front of an invisible house is pretty suspicious.

The Potters were hidden by the Fidelius Charm. You don't need extra protection when you have an -almost- unbreachable spell keeping your family safe. If Pettigrew hadn't revealed the secret to Voldemort, the Potters would've been safe as long as they were inside the house.

As noted by Roberto, they were hiding under the Fidelius charm. It's a bit hazy in the books as to what can break the Fidelius charm and/or bypass it (if you set off a bomb that would destroy the entirety of Godric's Hollow, would it affect a house under Fidelius?), and how much the Potters passed on to the Ministry about their location (given they already know there were possible traitors). Thus, it's not unreasonable to suppose that the Ministry would not be certain that the Potters were indeed in Godric's Hollow versus a different safehouse.

And yes, that opens up a whole new set of questions as to why the Potters would choose a location that people knew the general location of versus picking a location in another town, but you can probably chalk that up to them trusting in the magic to protect them, and not wanting to completely uproot themselves for the duration of the war, which was still ongoing. There are always tradeoffs in security.

1. Dumbledore wasn't sure the Potters were the target.

The Potters weren't the only one who had a child at the end of July; the Longbottoms also had a child (Neville) who fulfilled all the conditions of Trelawny's prophecy. But it was Voldemort who chose Harry.

“You are forgetting the next part of the prophecy, the final identifying feature of the boy who could vanquish Voldemort.... Voldemort himself would ‘mark him as his equal.’ And so he did, Harry. He chose you, not Neville. He gave you the scar that has proved both blessing and curse.” “But he might have chosen wrong!” said Harry. “He might have marked the wrong person!” “He chose the boy he thought most likely to be a danger to him,” said Dumbledore. “And notice this, Harry. He chose, not the pureblood (which, according to his creed, is the only kind of wizard worth being or knowing), but the half-blood, like himself.
_{Harry Potter And The Order of The Phoenix Chapter 37: The Lost Prophecy}

2. No one knew that Voldemort would make such a move.

No one expected Voldemort to do such a thing, because, he didn't know that a prophecy even existed. Thanks to the snitch, in this case, Severus Snape who only overheard the first half of the prophecy rushed to inform his master.

... Of course, I had not dreamed, when I set out to meet Sibyll Trelawney, that I would hear anything worth overhearing. My — our — one stroke of good for- tune was that the eavesdropper was detected only a short way into the prophecy and thrown from the building.”

“So he only heard . . . ?”

“He heard only the first part, the part foretelling the birth of a boy in July to parents who had thrice defied Voldemort. Consequently, he could not warn his master that to attack you would be to risk transferring power to you — again marking you as his equal.

Snape was the one who made Voldemort think the prophecy was about the Potters when he requested Voldemort to save Lily.

Dumbledore flicked his wand. Though leaves and branches still flew through the night air around them, silence fell on the spot where he and Snape faced each other.

“What request could a Death Eater make of me?”

“The—the prophecy. . . the prediction. . . Trelawney. . . ”

“Ah, yes,” said Dumbledore. “How much did you relay to Lord Voldemort?”

“Everything—everything I heard!” said Snape. “That is why—it is for that reason—he thinks it means Lily Evans!”
_{Harry Potter And The Deathly Hallows 33: The Prince's Tale}

3. The Fidelius Charm

Most of the Aurors and wizards who fought against the Dark Lord went into hiding and some were put under protection, i.e, the Fidelius Charm. Getting Aurors to guard these wizards/Aurors would have been pointless as the protectors themselves were being hunted by the Death Eaters.

In case of the Potters, they had the Fidelius Charm that protected them; they just trusted the wrong person.

The Ministry was not a great source of resistance, the Order knew they had a traitor in their midst, and Voldemort was extremely dangerous

1. This Ministry of Magic was not, in Dumbledore's view, a sufficient obstacle to Voldemort's rise. This is clear both because the Ministry and the Death Eaters were more or less at war, but Voldemort continued to rise in power and influence throughout, and also because Dumbledore saw fit to build his own organization specifically to oppose Voldemort.

   That's not to say that they couldn't have done anything to help, of course, but I don't recall any instances of the Ministry opposing Voldemort successfully at all-- if a few professional aurors as bodyguards were sufficient to keep alive someone Voldemort wanted dead, he wouldn't have been the threat that he was.

2. The Order might have tried to coordinate such a thing, but instead decided to work through misdirection and hide the Potters via the Fidelius charm and a-- this was considered to be better because only one person could know the secret information, and by choosing a less obvious person to hold the secret no amount of violence or pressure that the Death Eaters could bring to bear would reveal it.

   But they knew at the time that at least one of their members was a traitor, which was the whole plan's undoing. Even if they had opted for any other plan, including bodyguards, it would also have been subverted and for the same reason. Controlling and hiding information was the plan they went with, and that's harder to achieve as more people gain knowledge of the plan (as would be necessary in getting the Ministry to dispatch aurors), as well as when people engage in unusual behavior (such as taking unusual guard duty).

3. An important thing to remember is that, prior to his attack on Harry, Voldemort essentially never lost. His minions did fail from time to time, but if Voldemort went somewhere to do something, that thing happened. Most efforts to protect people from the Death Eaters must have failed-- they were gaining influence and power continuously until that night at Godric's Hollow, becoming a force which not only could contend against the entire wizarding community of the United Kingdom, but were winning.

   A couple more bodyguards is like a few more blades of grass in a lawnmower's path: present, but not really something that will stop (or even impede) the lawnmower.