The political system in Switzerland is known to increase stability, not reduce it.
The way I see it, this is down to two factors:
1. Since Switzerland does have multiple parties and all of the bigger ones a represented in the federal council, there is more compromise and decisions made by consensus. This in turn leads to less dramatics shifts after a term is up and some politicians are replaced.
In contrast in the US, where you could have a democratic president and parliament coming in after a term of a republican majority and president (or vice versa). It seems likely, that the new powers to be would set about undoing some decisions made by their predecessors. At the very least you'd have a rather dramatic course change at hand.
2. It is very easy to collect enough signatures for a referendum (50000 signatures within 100 days of the law being passed in parlament) and for every change to the constitution there is a mandatory referendum (no signatures needed, it will brought to a public vote).
This means that any controversial law can be brought to a public vote. Which more or less prohibits sudden drastic changes and promotes more incremental change, which brings more stability.
On the other hand, there might be something to the Idea, that direct democracy reduces stability. Basically it is the flip side of 2. above: it is also quite easy to gather 100000 votes to establish a popular initiative.
The parties have picked up on that and often introduce controversial initiatives to further their election campaigns.
There are not many safeguards in place, so unfortunately there was an increase in badly drafted amendments in recent years. Different parties have brought forward initiatives that contradicted other parts of the constitution.