The BBC says it "regrets" causing offence by asking listeners to vote on whether two characters should abort their baby.
In the radio drama, characters Mike and Vicky Tucker recently learned their unborn child had Down's Syndrome and faced a dilemma over what to do next.
On the programme's Facebook page, fans complained the vote was "distasteful", "disturbing and upsetting".
The BBC admitted the issue was "too complex and sensitive" for a poll.
The online vote was featured on The Archers website last week. It has since been replaced, but a link remains on Facebook with the message: "Mike and Vicky's dilemma makes up this week's vote: should they go through with the pregnancy?"
Among the responses, Helen Ward posted: "This poll is incredibly insensitive and inappropriate and should be removed."
Jill Anthony-Ackery added: "I was very surprised when I saw this poll. The storyline is hard, the considerations are complex and any decision will be fraught with doubts - not a scenario which can be answered by yes/no, by people who have never been there."
One day after the poll was published, the BBC posted in response: "Sorry you feel this way about the current vote. The polls tend to reflect the storylines that are most talked about in the programme, and this is Vicky and Mike's dilemma. The result of the poll doesn't affect the outcome of the storyline."
It later added the poll was "often about a dilemma that faces a character - eg should Adam leave Home Farm".
"Mike and Vicky's decision is more awful than this, of course. But they are still faced with a stark choice one way or the other. So we didn't think that representing that choice on the poll was trivialising the issue," it said.
The vote was taken down on Monday, after its scheduled one-week run.
A BBC spokesman said: "The Archers storyline on Mike and Vicky's pregnancy has been well received by the audience and raises a number of important issues about Down's Syndrome, informed by the advice and expertise of the Down's Syndrome Association.
"However this issue is too complex and sensitive for an online poll and we regret any offences the poll may have caused."
Despite the controversy, Xanthe Breen from the Down's Syndrome Association praised the Radio 4 show for its handling of the storyline.
"Due diligence has been excellent and producers have made sure the storyline is accurate in what would happen to a woman who goes through the screening process," she said.
"The storyline is very relevant and encourages people to talk about it. We encourage people to keep listening as the story unfolds."