You may want to take a look at these previous threads on this topic:

• How did the Basques maintain their language through Roman occupation and influence, and up until the modern era?
• What are some explanations for why the Basque language has survived to this day?
• Considering the length of time the Basque area was under Roman rule why is their culture/language so different from their neighbors?

The consensus seems to be that the mountainous geography of Basque Country played a large role. In the first thread, /u/Tiako and /u/keyilan note that mountainous regions are historically good at preserving linguistic diversity, and compare Basque to Paleo-Sardinian, another non-IE language and possible language isolate spoken in a mountainous area that became extinct in the 2nd century AD or so.