GREENVILLE, S.C.—When Ruth Silver was watching last week’s Republican debate in her Wantagh, N.Y., living room, she was so impressed with Carly Fiorina’s “class and poise, I wanted to stand up and applaud.”

Ms. Silver, 71 years old, said the former Hewlett-Packard executive’s performance was so strong she began rethinking her support for celebrity businessman Donald Trump.

For now, Ms. Silver is sticking with Mr. Trump but she is part of a shrinking pool: Female voters’ support for the first-time candidate dropped 12 percentage points among likely GOP voters after last week’s CNN debate, according to a CNN/ORC poll conducted Sept. 17-19. The poll has a margin of error of plus or minus 3%.

That decline in support helped drive down Mr. Trump’s standing in the primary field. Although still the front-runner, his backing tumbled by eight percentage points, to 24% from 32% in a CNN/ORC poll conducted Sept. 4-8. Of those who tuned in to watch the debate, 31% of the likely GOP voters said he did the worst job—the highest percentage of any candidate.

The Trump campaign didn’t respond to requests for comment on Tuesday.