So which part of the German system makes it so stable? Is it their election model? Or is it just that German parties are inherently more stable and scandal free?
First, and foremost there is no limit on the number of terms the chancellor can take in Germany, other countries use this mechanism to limit the length of a premiership.
Second, there are about 5-6 parties in parliament with one major party standing out, the CDU. Representing the center-right part of the political spectrum, it often scores ~40% in parliamentary elections, making it highly probably to be part of any governing coalition and even more probable to provide the chancellor, which usually comes from the biggest party in a party-coalition.
Third, the CDU is known for supporting its party leaders (and chancellors) for a long time (Konrad Adenauer, Helmut Kohl, Angela Merkel all served much longer than 10 years). Big scandals are indeed rare (at least during the time of their premierships) and competitors within the party are usually weakened by the current leader until a turning point (a defeat, a scandal) arrives.
So there you are: No inbuilt limitation, a single, very strong party and a tradition of not changing the leader.
It's not that uncommon though, Margaret Thatcher was prime minister for 11 years, Tony Blair for 10 years and Vladimir Putin is already in his third presidential term (all in parliamentary states).