The public's confidence in the economy slipped again this month, according to a Washington Post-ABC News Poll, and four of 10 Americans are worried they may suffer financially because of the failure of a bank or thrift institution.

Asked where they believe the economy is headed, 35 percent of the poll respondents said they think it is getting worse, 27 percent said the economy is improving and 37 percent said it is staying the same. A random sample of 1,506 adults were interviewed for the poll between last Thursday and this Monday.

The responses continue a trend of increasing pessimism about the economy that began early this year. In February, 41 percent of the poll respondents said they believed the economy was improving, while 25 percent thought it was getting worse.

However, the poll didn't show much change in how people assess their personal financial prospects, as opposed to the outlook for the overall economy. Asked how they will be doing a year from now, 34 percent said better, 16 percent said worse and 48 percent said about the same. This response has been essentially unchanged since mid-1984.

For the first time, the poll sought to measure the public's concern about the record pace of bank and savings and loan association failures. Fourteen percent of the respondents think it is very likely they would be hurt financially by a failure, 29 percent said it is somewhat likely, 27 percent said somewhat unlikely and 27 percent said very unlikely. The remainder did not answer or had no opinion.

Another question asked respondents was whether they expect their family earnings to grow faster than inflation, just keep up or fall behind.

The responses show that 13 percent of adults expect to do better than inflation, 54 percent expect to keep pace and 30 percent believe they will fall behind inflation.