There is ample evidence that the Ringworld is very old (millions of years); the evidence includes, for example, the level of divergence of the humanoids populating the Ringworld from Earthly humanity. However, there is also evidence of decay that cannot have been going on for nearly that long. Louis cites two specific elements of the decay that seem to be relatively recent:
All the peaks of foundation material showing through the rock...
Along their voyage, the characters observe a number of locations where the underlying scrith that makes up the backbone of the Ringworld has been exposed by erosion. Louis knows enough about erosive geology to recognize the the erosion patterns he sees are relatively recent. If they had been proceeding at their present pace for the entire lifetime of the Ringworld, then most of the soil would have been gone from the entire structure.
... and the fall of civilization only fifteen hundred years old!
There had been an advanced civilization of the Ringworld, but it had collapsed—and quite recently. They know that because a fair amount of technology (where it possessed an autonomous power source) is intact and functioning. Again, it would be very peculiar if the Ringworld had been functioning for millions of years, but it just coincidentally happened to have had a major disaster, leading to the collapse of an advanced civilization, only thousands of years ago.
These things suggest that something relatively recent (only thousands of years ago) upset the ecological balance on the part of the Ringworld the characters were exploring. Louis concludes that it was probably the presence of the two holes in the scrith (which might have been caused by a single event with multiple impacts) are responsible for the disturbance.
The fact is that a substantial amount of air is indeed leaking out of at least one of the holes (the one with the eye storm above it). That is producing the racing winds that have started wearing the soil off the surface of the scrith. The amounts of atmosphere loss involved could not be sustained indefinitely. Over the lifetime of the Ringworld, the losses would be ecologically catastrophic; this is another piece of evidence that the damage is relatively recent. However, one of the key points about the Ringworld is how vast it is; the effects of the lost air are not going to be felt for a long time.
Regarding Fist-Of-God Mountain, my recollection is actually that it is so large that there is not significant air loss through the hole in its center. Remember that at the edges of the Ringworld, the air is only held in place by tall walls. The impact mountain is, I believe, actually taller than the side walls, so air losses up its slopes are minimal.
