His best result during the season was a quarter-final appearance at the 2001 Irish Masters losing to O'Sullivan. He also did not qualify for the next two years World Snooker Championships. Davis failed to qualify for the 2001 World Snooker Championship, the first time he had not appeared at the event after he debuted in the 1979 event. He lost to Andy Hicks in the last round of qualifying 6–10. After the loss, he contemplated retirement, but said that it would be the "easy thing to do". Since he still enjoyed the challenge of professional play he continued into the 2001–02 snooker season and reached the semi-finals of the 2002 LG Cup and the quarter-finals of the 2003 Irish Masters the following season. However, Davis was unable again to qualify for the 2002 World Snooker Championship, losing to Robin Hull in the final round of qualification 8–10.