NEW YORK, Oct 21 (Reuters) - The U.S. secured overnight financing rate (SOFR), the Libor replacement preferred by the Federal Reserve that measures the cost of overnight cash in the repurchase (repo) market, stayed at 0.03% for a second straight day after holding steady at 0.05% for the last four months.

Analysts attributed the unexpected decline to recent volatility in short-dated Treasuries and excess cash from government-sponsored enterprises (GSEs).

The current SOFR number reflects Wednesday's rate. The New York Fed publishes the SOFR each business day at 8 a.m. ET.

The drop to 0.03%, which started on Tuesday, was unusual and caught market participants by surprise. SOFR was at 0.05% since June 17, a day after the Fed raised the reverse repo rate and the interest rate on excess reserves, aimed to keep its overnight benchmark rate from falling too low.

The decline in repo rates followed a surge in short-positioning in short-dated Treasuries, analysts said, as expectations grow for an earlier-than-expected Fed rate hike next year. To short 2-year notes, for example, investors borrow them from entities such as money market funds, sell them, and repurchase them later.

These U.S. 2-year notes became what are known as "repo specials," referring to securities that have overwhelming demand in the repo market. Competition to buy or borrow a special security prompts potential buyers to offer cheap cash in exchange.

On Thursday, U.S. 2-year notes traded the most "special" among Treasury securities, with repo rates of borrowing it at -1.56%. Market participants were willing to pay interest on money lent to borrow the 2-year note, instead of the borrower of cash who usually pays interest for the loan.

Also, on the 18th of each month GSEs like Fannie Mae and Freddie Mac invest cash in the repo market as they receive mortgage payments from homeowners. That typically pushes repo rates lower. When they make their principal and interest payments on the 24th, that GSE cash leaves the market, pushing repo rates higher.

"The SOFR decline leads to questions about the stability of the rate set to become the new U.S. dollar benchmark once libor goes away," said Dan Belton, fixed income strategist, at BMO Capital in Chicago.

"A lot of investors were skeptical of the rate to begin with, mostly because of its lack of a credit component. So the fact that it can drop so far within the Fed's target range, just 3 basis points from the bottom, and unexpectedly, adds to the questions about the rate's shortcomings as a benchmark." (Reporting by Gertrude Chavez-Dreyfuss in New York Editing by Alden Bentley and Matthew Lewis)