Is it pure luck that the voyager 1 survived to travel beyond our solar system in interstellar space?

A thing works fine until something goes wrong.
As far as I can see, the main external risks of the voyage were the radiation belts of Jupiter and Saturn, but those were already survived by the Pioneer 10 and 11 missions. After the planetary fly-bys, there are close to nothing external affecting the spacecraft.
The important risks therefore lies in the potential failure of of one of the spacecraft’s subsystems:

Power
The power source of the Voyager missions was an RTG. This requires no moving parts, and the decay of radioactive isotopes is not dependent on any external factors. This will probably work just fine until the power level has decreased enough.

Computer hardware
A computer has multiple potential weaknesses, the most common ones being overheating and memory malfunction, like what happened on the Galileo mission.
Radiation in outer space will over time slowly degrade electronic components. Magnetic memory will over time degenerate anyway.
It seems like what eventually will likely cause the Voyagers to fail is their nearly four decade old electronics.

Manoeuvring
The probes needed propellant for changing attitude, as well as for trajectory corrections. Corrosive propellant staying in the tanks for years are a major cause of spacecraft failures. See for instance the Akatsuki probe.