John R. Evans' second term as a member of the Securities and Exchange Commission is scheduled to end Sunday, and the White House hasn't indicated whether it intends to nominate him to the third term he wants.

This is not the first time the former academic has been left in bureaucratic limbo. In 1978 the Carter administration waited a year before reappointing him. As he did then, Evans will continue to serve now until an appointment is announced.

During the past decade Evans has gained a reputation as the "conscience of the commission" because of his tough attitude, and in the process has earned the enmity of the securities industry on such issues as ending fixed commissions and off-board trading. His stance may not be popular with the Reagan administration, which has been trying to curry favor with Wall Street.

It is also unpopular with SEC Chairman John S.R. Shad, a former securities lawyer. His aides say he wants to replace Evans with someone who will vote on his side more often. Shad reportedly has told the White House that he supports Charles C. Cox, the SEC's chief economist since last September, for the seat.

Meanwhile, some of Evans' colleagues are waging a strong lobbying campaign for his renomination. A group of 23 high-powered Washington securities lawyers recently sent presidential aide James A. Baker III an endorsement. Evans' backers also include Sens. Jake Garn and Orrin G. Hatch, both Republicans from Utah, his home state.

PAYING FOR THE PAYOFF . . . The SEC has proposed a controversial change in the way investment advisers are compensated. It would reward them for taking risks that pay off, but would not penalize them for the risks that don't.

Those managing the accounts of "financially sophisticated" investors with at least $150,000 would be entitled, if the client wishes, to charge a percentage of his capital gains.

Now, advisers earn a fixed fee regardless of the outcome of the investment. Compensation based on portfolio performance now is permitted only under very limited circumstances.

The proposal is controversial because it goes against a 40-year tradition. When the Investment Advisers Act of 1940 was drafted, Congress said that one-sided fees were tantamount to "heads I win, tails you lose." In this era of deregulation, the SEC wants to know whether sophisticated investors should be allowed to negotiate commissions with their brokers as a way of encouraging them to invest more aggressively. The agency is seeking public comments.

OFF THE SHELF . . . Shelf registration of stock offerings is not working well and should be scrapped, commissioner Barbara S. Thomas says. The experimental procedure, which allows securities to be offered on a delayed or continuous basis, was begun in March, 1982, and is scheduled to end Dec. 31.

Thomas contends that shelf registration does not allow the individual investor to get timely information about stocks being offered and that underwriters don't have time to research them. As a result, institutions are becoming the dominant buyers of new offerings and the business is being concentrated in the hands of a few major underwriters.

She says she thinks, however, that shelf registration should continue for bond offerings, which are less risky than stock offerings.