A weariness of and diminishing public response to frequent requests for charity.
This term originated in America in the 1960s. The first reference I can find to it is a quotation from Albert W. Farmer, the national director of CWS Community Appeals in the Indiana newspaper The Vidette-Messenger, in November 1967:
"More people are hungry today than ever before. Many Americans have compassion fatigue - tired out with all the repeated calls to do good."
In the UK the phrase is associated with Sir Bob Geldof who highlighted the many public appeals he had made himself. In an interview for The Guardian in May 2003 he said:
"Even I'm sick of myself ... I'm that quarter-page Oxfam [advertisement] in the Guardian, always asking for money."