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Texas Gov. Rick Perry remains the tenuous frontrunner for the Republican presidential nomination, despite enduring the toughest stretch of his seven-week-old campaign, according to a new CNN/ORC International poll released Monday.

Perry leads former Massachusetts Gov. Mitt Romney, 28 percent to 21 percent, according to the CNN poll. Former House Speaker Newt Gingrich is third at 10 percent, with all other candidates in single digits.

The poll represents a slight tightening of the race. Perry's seven-point advantage is down from a 12-point lead two weeks ago.

There are other red flags for the Texas governor in the poll data: The poll shows a striking, 20-point gender gap is developing in the GOP race. Perry holds a 17-point lead among men, while Romney leads by four points among women. Two weeks ago, Perry led Romney by double-digits among both men and women.

Perry's numbers are also dropping among those Republicans who attended college -- from a 13-point lead over Romney earlier this month to a scant, one-point edge now.

Another troubling sign for Perry: His numbers in the general election haven't moved, and Romney remains the stronger GOP candidate against President Obama, according to the poll. Perry trails Obama among all registered voters, 51 percent to 46 percent, exactly where he was the weekend he launched his campaign, the last time CNN tested the two head-to-head.

The Obama-Romney matchups numbers are also identical to the previous poll, conducted in early August. But Romney runs neck-and-neck with the president, trailing by just a point.

Obama's approval rating ticked up two points in the last two weeks, to 45 percent, a change that is within the margin of error. A majority continues to disapprove of his job performance.