When something is astonishing or astounding, it causes great surprise or amazement. It overwhelms you because it is so impressive. In other words, astonishing/astounding carries a positive connotation, unless you are using the words in a sarcastic way.
- The psychologist pulled strings to enroll in one of these trials. She was, by nature, effortlessly persuasive, and her illness had made her bold. She enrolled in a Gleevec trial at a teaching hospital. A month later, her tumors began to recede at an astonishing rate. Her energy reappeared; her nausea vanished. She was resurrected from the dead (New York Times, October 29, 2010): Here, astonishing means amazing/impressive/great.
- Senator Donie Cassidy has apologised for saying it "wasn't easy for senators with families to get by on €65,000 a year". This was in response to Senator David Norris. Mr Norris said it was "astonishing" for any politician to have suggested €65,000 was hard to live on at a time when "people are losing their jobs, are living on the minimum wage of €8.60 per hour and cannot pay their mortgages" (Independent, October 30, 2010): This is a good example of how you can use astonishing in a cynical way. Note how the author put the word in quotation marks, clearly indicating that he is being sarcastic.