In "The Swiss Family Robinsons", what enabled the Robinsons to not only survive but thrive?
The Robinson family thrived on the island through their faith, ingenuity, and incredible luck.
Obviously, their faith was very important to the Robinsons. It gave them a commitment to excellence, as working for God, not just for themselves. It also gave them a sense of indestructibility, in the sense that they felt that they would not fail in surviving as long as God willed it.
They were extremely creative as well. They used the materials on the island in unusual yet effective ways to "raise their standard of living" to a high level.
They were also unbelievably lucky (even unrealistically so, one might say) in the materials that survived the shipwreck, as well as the products of the island itself. The vast variety of flora and fauna (no explanation of how such variety of animals came to exist on such a remote location) provided them the means to develop many new technologies.
All in all, the Robinsons viewed their time on the island as their destination, rather than a roadblock. Their purpose was to colonize, so they resigned themselves willingly to colonizing a spot not of their own choosing, but one which served very well.