This happened to me twice last summer, although I wouldn't say that it broke off so much as SHOT off. Never found it either time. Using a Park floor pump both times. I chalked it up to the quality of the tube. I believe they were both Q-Tubes, so I avoid those now.
The Warrior Princess: 2008 Jamis Xenith Pro / Bontrager Affinity 1 (men's)
2006 Trek Fuel EX 9 / Bontrager Race Luxe
2007 Trek 520 / Serfas Terazzo
Amelia Pond (She travels long distances, has great adventures, and she's a redhead): 2007 Trek Pilot 5.0 / Bontrager Affinity 2 (men's)