I remember well the last big San Fransisco earthquake in 1989. There were a lot of collapsed buildings and structures. At first, the engineers and soil engineers were baffled. The soil was a thick, heavy, solid sand-clay. It had been compacted to what they had thought was its maximum compaction, over time. The heaviest of buildings, built upon it, just didn't sink. It had a very high load factor.
In fact, when digging foundations, you could dig at pretty much a 90 deree angle slope side wall, for quite a depth, without the soil collapsing. Almost as steep and stable as a rock slope.
Yet, many very solid buildings actually sank and tilted in the soil.
What they found, after some experimentation, was that under the high frequency of the shaking during the earthquake, the soil essentially liquified. The buildings were no longer on a solid footing, they were in quicksand.
So, in fact, you can have a very stable mountain with a fairly steep slope, as long as you have some mechanism by which the footsteps of the humans create a very high frequency local vibration. How you produce this effect, is a seperate issue. Perhaps there is something about the metabolism of your inhabitants that cause them to shake constantly and violently, like a hummingbird must vibrate. Thus, the mountain would remain stable up until they tried to climb it. Then, it would turn as slippery as slushy water, but only where their footsteps landed.
See this reference for a description of soils that are mose susceptible.
Poorly drained fine-grained soils such as sandy, silty, and gravelly
soils are the most susceptible to liquefaction.
Here is a link to liquefecation of clayey soils, that can cause landslides.
Research was conducted on artificial clay–sand mixtures and natural
clayey soils collected from the sliding surfaces of earthquake-induced
For the artificial clay–sand mixtures, it was found that the presence
of a small amount of bentonite (≤ 7%) would cause rapid liquefaction,
while a further increase in bentonite content (≥ 11%) produced the
opposite effect of raising soil resistance to liquefaction by a
significant degree. It was demonstrated that the bentonite–sand
mixture was considerably more resistant to liquefaction than the
kaolin-, and illite-mixtures, given the same clay content. The test
results of plastic soils revealed the significant influence of
plasticity on the liquefaction resistance of soil.