However, SolarImpulse is shooting for an eventual round-the-world, non-stop flight. They're even designing a new plane:
There's some major logistical challenges to go along with the technical challenges:
1) They need at least two pilots to spell each other (which means more weight)
2) The new plane would have to go faster - at 70kph, flying 40,000 km would take 24 days
3) There would need to be room for food and water (which, again would mean more weight)
4) They would need, uh, facilities (again, more weight)
I guess you could solve all of these problems by simply scaling up the plane. I think that might also break the record for longest wingspan...