Q:

Why didn't Voldemort create a Horcrux with a Gryffindor heirloom?

Voldemort was said to be very interested in the four founders of Hogwarts. He created a Horcrux from the Ravenclaw diadem, the Hufflepuff cup, and the Slytherin locket. Did he try to find a Gryffindor relic to complete the set, or did he not bother? 
I can't see him giving up on such a task, but maybe there was insufficient time.
Gryffindor's sword was hiding 'inside' the Sorting Hat, but a famous family usually has some other heirlooms too.
If there are no canon answers I'd be interested in your own speculation!

A:

From Dumbledore himself in HBP, while discussing Voldemort's horcruxes with Harry:

"I am confident, however, that the only known relic of Gryffindor remains safe."
HBP, Chapter 23, p505, Scholastic Edition. Emphasis added

So, I believe we can take this as confirmation that no other family has another heirloom. Else, Dumbledore and other magical historians (like Bagshot) would've known about it.
And, as we know, only Gryffindors can take the sword from the Sorting Hat. Voldemort, as a Slytherin, wouldn't be able to even if he wanted; he's really better off giving up since he is unable to acquire it by himself. Though he may be able to trick a Gryffindor into getting it from the Hat for him, remember that Voldemort likes to operate alone, especially when it comes to his horcruxes. So I don't think that plan would appeal to him.
(It's worth noting too that the Sorting Hat is a relic of Gryffindor's. I don't know if it can be turned to a Horcrux tho, given its current enchantment.)

A:

I think the answer is simply that it would be impossible to protect, seeing as ANY Griffindor could pull the sword out of the hat. No matter what protections he put on it, any one of his enemies who was in Griffindor would have easy access. It would never be safe.

A:

Even though he probably didn't realize it, he did have a Horcrux in each house.

The Locket/Slytherin.
The Cup/Hufflepuff.
The Diadem/Ravenclaw.
Harry Potter/Gryffindor.

