I dont think that there is any such limitation on selection of object after live trace , may be you haven't ungrouped properly ....
1) edit--> select All
and then check
If you having difficulties selecting the paths on the canvas try selecting them in the Layers Panel using the shift key as well.
Selecting them all did not improve the result
In the layers panel I had only one layer, so again not much help.
What I noticed though is that I have to hit "select" on the area inside the path not the contour per se and then all paths get selected.
Thank you. Avi