there are a few possible answers and I will review them here:
Voldemort intended to come back to life and rule the wizarding world within a year. therefore having one of his death eaters work at Hogwarts was unnecessary after the year past.
Quirrell- Was Supposed to retrieve the stone within the year. Voldemort would have than return to full power and have his death eaters with him. However, that might take time and Voldemort would still need for the meantime a spy in Hogwarts- No worry, Quirrell taught muggle studies before DADA, and it would be quite reasonable for him to switch back to a subject he isn't afraid of.
I also won't be surprised if Voldemort would just leave Quirrell to die at the end of the year, since in Voldemort's opinion Quirrell is a fool and a puppet who needs to be possessed and has no use to him after he returns to power.
He left Quirrell to die; he shows just as little mercy to his followers as his enemies.
BCJ- was pretending to be Moody, who probably insisted to Dumbledore to teach at Hogwarts only for a year, and it would look suspicious if he changed his mind.
Yeah, I'm staying just the one year. Special favor to Dumbledore.... One year, and then back to my quiet retirement."
However, there might have been a plan to keep Moody (BCJ) at Hogwarts for another year, since he will prove as a useful spy. that plan was probably changed when Snape came to Voldemort at the end of GOF, and Voldemort kept Snape as a spy rather than BCJ, for 2 reasons:
A- It will be suspicious if the retired Moody who just told Dumbledore he'll work at Hogwarts for only one year as a special favor would change his mind and want to work there more. (There is also a big chance Dumbledore recruited Moody specifically for one year, since he knew about the DADA curse and would rather Moody would leave on his terms than Voldemort's)
B- It will be really suspicious if after 25 years of a different DADA teacher, Moody would break the streak. Dumbledore will surely investigate into it, exactly the thing Voldemort doesn't want.
"You see, we have never been able to keep a Defense Against the Dark Arts teacher for longer than a year since I refused the post to Lord Voldemort."
There is also a chance Voldemort's DADA curse was permanent, though we can't prove that.
Also, in both Quirrell's and BCJ's case, Voldemort was in a very weakened state and didn't have the power to remove the curse.
In conclusion: Voldemort didn't remove the curse because it would be unnecessary, undoable, required power Voldemort didn't have at the time and raise suspicion.