I seem to remember Tyrion making a comment about how little the Valyrian roads have degraded since the Doom. Does the text mention anywhere what exactly the roads are made of, or rather, what is preventing them from degrading?
I think I found what you are looking for:
According to the wiki:
"At the start of his journey to Volantis Tyrion Lannister takes the opportunity to have a closer look at the Valyrian road that he and Illyrio are traveling on. It runs as straight as a spear to the horizon. It is a ribbon of fused stone raised half a foot above the ground to allow rainfall and snowmelt to run off its shoulders. Tyrion muses that unlike the muddy tracks that pass for roads in the Seven Kingdoms, the Valyrian roads are wide enough for three wagons to pass abreast, and neither time nor traffic mar them. They still endure, unchanging, four centuries after Valyria itself had met its Doom."
The roads are made from fused stone that is built in a way that allows rain and snow to quickly run off the sides.
We can reason that this is a huge factor in its preservation and its condition.
As for if there is magic involved, the wiki isn't clear, but according to another page of the wiki Valyrian steel is magical. So there is a possibility some magic was used to create the roads.
The Valyrian roads are made of fused stone and raised off of the ground to allow for drainage. They are usually wide enough for 3 wagons to pass side by side and are extremely straight.
During one stop, he used the time to have a closer look at the road. Tyrion knew what he would find: not packed earth, nor bricks, nor cobbles, but a ribbon of fused stone raised a half foot above the ground to allow rainfall and snowmelt to run off its shoulders. Unlike the muddy tracks that passed for roads in the Seven Kingdoms, the Valyrian roads were wide enough for three wagons to pass abreast, and neither time nor traffic marred them. They still endured, unchanging, four centuries after Valyria itself had met its Doom. He looked for ruts and cracks but found only a pile of warm dung deposited by one of the horses.
A Dance with Dragons, Tyrion II
There's no information on how the roads are made but since there are no cracks in them after four centuries and they are fused stone it isn't unlikely they are made from melting stone. Especially considering that dragonfire is hot enough to melt stone and that Valyrians had dragons of course.
Stone does not burn, Harren had boasted, but his castle was not made of stone alone. Wood and wool, hemp and straw, bread and salted beef and grain, all took fire. Nor were Harren's ironmen made of stone. Smoking, screaming, shrouded in flames, they ran across the yards and tumbled from the wallwalks to die upon the ground below. And even stone will crack and melt if a fire is hot enough. The riverlords outside the castle walls said later that the towers of Harrenhal glowed red against the night, like five great candles...and like candles, they began to twist and melt, as runnels of molten stone ran down their sides.
The World of Ice and Fire, The Reign of the Dragons: The Conquest