They had driven ten miles when the car broke down.
They had been driving ten miles when the car broke down.
I am sure that the first sentence is correct. The second action happened when they had already covered ten miles. But I wonder if the second sentence is possible.
Both are fully grammatical, and both are completely natural. As with many questions about the use of perfect and continuous aspects in English, the difference is not about the circumstances but about how the speaker is choosing to refer to the temporal structure of the situation.
The first treats the driving as something which had finished (stopped) when the breakdown occurred. The second treats the driving as a process which was continuing through the breakdown. Both are equally valid, but give a slightly different flavour.
I prefer:
They had been driving (for) ten miles when the car broke down.
This one is better because there is an implication that they would have driven further, but could not because the car broke down.
As @Ustanak said, the first one is not clear. Perhaps they drove ten miles (let's say to the store and back). Then the next time they started the car, it wouldn't.
More context is needed here.
Only a few miles....only a few feet... etc are not durational measurements but "completional" (maybe that word doesn't exist) and as such are incompatible with the progressive/continuous. They're compatible with the perfect.
not OK The new skyscraper had been rising for only ten storeys when the steelworkers went on strike.
not OK I had been eating only three bites when I chipped a tooth.
not OK I had been taking only three sips when a fly landed in my glass.
not OK I had been climbing only three rungs when the ladder gave out.
OK I had been watching the show only three minutes when the TV went dark.
OK I had been taking that detour for only three weeks when the bridge was re-opened.
OK I had been snoozing in the back of the lecture hall for only three lectures when the news came that the professor had quit teaching to become a race-car driver.
To simple build on what has already been said, native speakers of English often opt for the past perfect continuous over the simple past perfect to place more emphasis on the actual activity. Your second example places more importance on the driving than the first example.
