As the system staggers out of a brutal winter season, city officials have taken Citi Bike’s operators to task over its persistent financial concerns, which have left the program hunting for new investors to support the system and pay for its long-awaited expansion. Yet a review of the program’s history suggests that a confluence of factors — wishful projections and political considerations, forces of nature and misadventures in paperwork — has imperiled the system.

In recent months, the program’s operators approached the administrations of Mr. Bloomberg and his successor, Mayor Bill de Blasio, about raising the cost of an annual membership, proposing rates up to $140, according to people with knowledge of the discussions. The cost is currently $95. The city has resisted any change, though there is a dispute as to whether the company can increase its rates unilaterally.

Officials acknowledge that any expansion of the program, including planned extensions to the Upper East and Upper West Sides, will almost certainly not come this summer.

On Wednesday, the company that operates Citi Bike, NYC Bicycle Share, said that its general manager, Justin Ginsburgh, was stepping down to go to work as an adviser to Peter Lehrer, a construction management executive.

The fate of the program rests in large measure with Mr. de Blasio, who said last week that he hoped to expand the system, but added that city budget money was “not on the table,” at least at the moment.