These type of long-term activations are hard to do with FMRI, since slow up-and-down drifts can be caused by signal drift AND by neural work. In such a case, I would definitely design the study to have at least a minute of unrelated active task (not "rest") at the beginning and end, so as to provide a baseline level for contrast. It would be better to also have some of this distractor task in the middle, too, but you probably don't like that idea. Then you would look at the turn-on and turn-off times of activity for voxels, and only accept as active those that correspond to the known task timing. Finally, in any one subject up-and-down drifts in activity could still be somewhat due to baseline drifting, so you have to end up with a consistent story when you combine multiple subjects.

This problem is similar to the one faced by people doing pharmacological FMRI (e.g., cocaine or ethanol administration). In these cases, they look for the turn-on times (no pun intended) and also look for voxels that fit a nonlinear model of the pharmacological dynamics they expect. Perhaps you don't have a learning model to fit. But you have to be careful, as the druggie FMRI people have been, or your results won't be convincing. Elliot Stein (formerly Medical College of Wisconsin, now NIDA) has done a lot of work along these lines.