More than a year before a key European banking-rescue program is set to end, banks are starting to lobby for a plan to replace the old one, a sign of how rickety the continent's financial system remains.

Starting in late 2011, the European Central Bank doled out roughly €1 trillion ($1.34 trillion) of emergency three-year loans to hundreds of European banks. The program, known as the long-term refinancing operation, or LTRO, was designed to save ailing banks that were struggling to borrow money through ordinary channels.

The program is widely credited with easing—at least temporarily—Europe's financial crisis.

The cheap ECB loans start coming due in early 2015. A growing group of bankers, investors and some policy makers are anxious about whether some banks, especially in financially shaky countries like Spain and Italy, will struggle to stand on their own once the loans mature.

Members of the ECB's Money Market Contact Group, a panel of bankers and analysts who advise the central bank, warned in their quarterly meeting earlier this month that the looming maturity of the loans is viewed as a "cliff" that is weighing on market confidence, according to a summary of the Sept. 3 meeting, which was attended by ECB President Mario Draghi.