It appears to be random. Two of the show's writers, Joe Pokaski and Aron Coleite, discussed this in an interview. Here are some of the interesting snippets:
Q: Now, also along this genetics line, shouldn't Nathan's other kids
(Claire's half-siblings) have powers? Or is that only guaranteed if
both parents are powered?
A: In genetics, nothing is guaranteed. A random mix of traits. Gregor
Mendel and all that. Do we have to have a biology lesson, too? Wasn't
the boring physics lesson enough?
In a separate session with the same site, this exchange occurred:
Q: Claire's new classmate West can fly. This brings up an interesting
question about the heroes - can two different people have identical
powers? And going back to Neal's theory above, does this necessarily
indicate a genetic link? Are Claire and the classmate going to end up
being the Luke and Leia of "Heroes?"
A: First off, Ew. And no, similar powers do not mean a genetic link.
We've seen that the existence of powers may be something passed on,
but the powers themselves are a crapshoot of sorts...
So the writer's appear to be happen leaving it as random as to why certain abilities are and are not passed on.
If you're interested, this Wikipedia page has an awesome list showing all the families in the show where multiple people have powers.
except in the case of Matt Parkman. There are other examples: Sylar and his father both have the same power, and Claire's mother Meredith and her brother Flint both have the same power (except that his flames are blue). – Crow T Robot Oct 21 '14 at 21:50