"He's got to do something and fast," said Loretta Walsh, a white city councilwoman and a supporter of the mayor. "This thing is reaching crisis proportions.
"When it comes to the black community, he can't seem to do anything right. It's almost as if he's been cursed."
Frawley disagrees with those who say his image is suffering among blacks, who make up 47 percent of the city's population.
The last few months have been anything but tranquil in this area. Consider:
* In 1985, Frawley commissioned a $42,000 police promotions test designed to help move black officers up through the ranks. The mayor repeatedly touted it as bias-free. But when the results of the exam were released in April, none of the black or Hispanic officers who took it had passed.
* Also last year, Frawley signed legislation establishing a civil rights
commission. But a year later, seven of the 14 panel members resigned, saying they refused to act as window-dressing for the mayor.
* On Oct. 22, Frawley complied with the recommendations of an independent police commission by appointing a member of his cabinet to investigate complaints of police brutality. But members of the police force have refused to cooperate, saying an outside investigator is a violation of the Police Bill of Rights. If the administration forces the issue, it will most likely end up in court.
"Progressive whites and young blacks voted for Frawley because he was smart and they thought he had a conscience," said Margaret Henry, the former chairwoman of the civil rights panel. "He hasn't lived up to the latter."
Susan Bohm, who was the first of the civil rights commission members to resign, said, "There have been so many issues relative to civil rights abuses that we were willing to address. But each time, the mayor said it wasn't our job. If police brutality wasn't our job, and police promotions wasn't our job, what was?
"It seemed that the administration just wanted us so they could say, 'We've got a civil rights commission.' But they didn't want us to do anything. It was all window-dressing."
James M. Baker, a Frawley supporter and the first black to serve as City Council president, says that the mayor has "a communications problem . . . an image problem. But really it's not a problem with the man and his program."
"In my opinion, he just needs time to grow into the office," Baker said. ''All new politicians need time to develop their public images. Actually, a lot of people in the political community, and in the black community, support him and what he's trying to do here."
The son of a Fulton, N.Y., assembly-line worker whose family never owned a home during his childhood, Frawley in 1972 became the first person in the country to buy a house through the federal urban homesteading program. He and his wife, Bonita, a remedial-reading teacher, bought the dilapidated house on the fringes of the downtown area for a dollar, renovated it and lived there for 11 years before moving to another home in downtown Wilmington.
Frawley served on the Wilmington school board from 1974 to 1978 and was president in 1978 when the schools were desegregated through a merger of the city and New Castle County systems.
He was on the City Council from 1980 to 1984.
Then, in 1984, he entered the Democratic mayoral primary against a field that included the City Council president at the time, Frank Vari, an old- school politician skilled at manipulating the city bureaucracy and always ready with Thanksgiving gift baskets for the poor. Also in the primary were two blacks, community activist Beatrice Carroll and Dwight Davis, the owner of a small employment agency.
Frawley edged Vari, the second-place finisher, by 217 votes, then got 75 percent of the votes in the general election.
"Frawley was never the favorite son of the black community," said Leo T. Marshall, chairman of the Democratic City Committee. "But after he won the primary, they seemed willing to give him a chance.
"Now that's fading fast."
In a recent interview, Frawley said, "When I ran for mayor, I ran as mayor for all the people - not just the businessmen, not just the yuppies, not just the blacks.
"But those blacks who've been in the city for a while, especially older blacks, are familiar with my commitment to civil rights," he said. "I run on my record, not away from it."
Frawley noted that when he served as school board president, the school system was 95 percent black and the faculty almost 100 percent black. "But I had a commitment. What I did on the board was done primarily to benefit blacks.
"Any criticism of my office - particularly from the minority community - is unfounded. Look at the things we've done for them."
In recent weeks, Frawley has taken steps to modify the police promotion system and has said he would name a new civil rights panel.
"We still stand behind the police exam," he said. "It's been proven valid over and over. But I was the first one to say I was disappointed with the results of it."
Late last month, he said, 41 police officers, half of them minority, graduated from a communications skills program designed to help them improve their performance on future promotion exams.
The administration has decided to keep the civilian complaints office but ''on a pilot basis," Frawley said. "It's there. We will see how much of a need there is for it. People must remember that I put together the commission that gave birth of the investigator in the first place."
He said the new commission would be more focused and would have an agenda. ''Before, they didn't have one and they faulted me for that. But I voted for the legislation establishing the commission while I was still a councilman.
"My opponents conveniently forget those things," he said.
Frawley said his problems with some blacks in Wilmington arose from the necessity of "saying no."
"You get negative fallout from that. You can't please everybody. But Harry Truman said, 'If you can't stand the heat, get out of the kitchen.' "
Frawley said that in a series of town meetings he held this year throughout the city, the response in the black community had been good.
One who would disagree is Rep. Al O. Plant (D., Wilmington), who recently launched a short-lived effort to impeach the mayor.
"Clearly, this man is insensitive, arrogant. He just plain does not care for black folks or the poor," Plant said.
A community meeting last month called by Plant to explore the impeachment possibilities was sparsely attended. Frawley later said that the effort was something that he "never took seriously."
Baker said the impeachment effort "had no realistic basis in law . . . but just the fact that it surfaced is not good."