As we see in the Battle of the Department of Mysteries, Harry Potter, Ron Weasley, Hermione Granger, Neville Longbottom, Ginny Weasley, and Luna Lovegood could penetrate the Time Room in the interior of the Ministry of Magic with ease, despite not yet having graduated from Hogwarts. Why didn't the Ministry put Aurors or protective enchantments to guard the Time Room, as it clearly contained magical items that were known to create great instability in the magical world?
tl;dr The kids didn't, the Death Eaters did.
You are right in saying they should have been under guard and Harry seems to agree with you there:
the six of them sprinted off down the hall, Harry in the lead, past the fountain towards the desk where the watchwizard who had weighed Harry’s wand had sat, and which was now deserted.
Harry felt sure there ought to be a security person there, sure their absence was an ominous sign, and his feeling of foreboding increased
Order of the Phoenix, Ch. 34, The Department of Mysteries
The Death Eaters need Harry to reach the Hall of Prophecy unhindered, therefore they would have to have removed every enchantment and personnel standing in his way. And the way that Voldemort showed Harry leads through the Time Room.
We therefore don't know if there generally are enchantments on the doors to the Department of Mysteries - or even if there usually are watchwizards making rounds after hours.
Considering the fact the Ministry is the entirety of the wizarding governing body (all branches of government - including on site law enforcement - are located inside the one building) there should be somebody working at all times including building security. The fact that nobody seems to do that is due to the special circumstances.