A self-perpetuating process which returns to its starting point with no improvement from when it was begun.
A vicious circle was the name given by 18th century logicians for a fallacious proof in this form:
A depends on B
B depends on C
C depends on A
This was alluded to in Edition 3 of The Encyclopedia Britannica, in 1792:
"He runs into what is termed by logicians a vicious circle."
A wider use of the expression was taken up by the medical profession and there are several examples from the early 19th century of it being used to describe conditions where one symptom affects another and the health of the patient steadily deteriorates.
The more general meaning of the phrase refers to any process where one event feeds off another but which seems trapped in a loop and eventually returns to its starting point, with no benefit gained. This imagery was employed in the 18th and 19th centuries to denote the circle of life and death. The emblem of a snake eating its own tail was commonly used in the iconography of Georgian and Victorian cemeteries - as in this example from Sheffield's General Cemetery.
The figurative, that is, not specifically logical or medical, meaning became established in the middle of the century; for example, this piece from Henry James' Notebooks, 1892:
"The whole situation works in a kind of inevitable rotary way - in what would be called a vicious circle."
The term 'vicious spiral' was later coined in the USA to denote a similar process but one which, after proceeding around the loop, ends in a worse position than before. This has been used most often in reference to economics; for example, this piece in The Syracuse Herald in March 1916, headed The Vicious Spiral:
"... we keep on putting up prices, raising wages so that people can pay the prices, raising prices again because people can better afford to pay them."
The converse to 'vicious circle' is 'virtuous circle', referring to a process of positive feedback. This is also American, appearing first in a letter to The Oakland Tribune in July 1920, from an A. S. Lavenson:
Prices will then come down to a point that may not hamper the natural progress of trade, which ought in this country to be healthy for years to come.
We might even be able to replace what has been termed the vicious circle with the virtuous circle.
Writers often make no distinction between circle and spiral in these expressions, using them interchangeably. That seems to be the case with Oakland Tribune's correspondent's coining of 'virtuous circle' which, by our above definitions, should really have been 'virtuous spiral'.