Mechanically, if that's cheaper/more suitable, I can see why it would be better. But it doesn't fit with the creator's intentions at all.
Concentration duration allowed her to make each punishment/learning-to-endure-pain session as short or as long as she desired.
If she had to chastise her pupil more than 12 times a day, she would have simply sacrificed the child to Lucifer.
Is the story-picture clear, or am I describing poorly?
Doh! That makes sense. Yes, I want the rod to be touching the person for the duration of the pain experience, and then at the end (when the rod is no longer touching bare skin and/or concentration is dropped) the target loses a fatigue level.
Is there any way mechanically to give a spell/effect a "necessary condition?" I can think of several examples in spells, but I'll cite just one: Murigen in "The Champion's Portion" in ToME has a spell that turns her into a fish. When casting the spell, she drapes a piece of chainmail over her forehead. The spell has sun duration, or ends if the chainmail is removed - spell effect ends when skin-contact is broken.
That's a spell, not an item, but it seems to me that many examples of spells/items go beyond the spell/guidelines/item creation rules, which are really quite limited and vague. I honestly wish that the spell creation guidelines were more detailed and specific, that we weren't forced to infer so much unspecified wisdom from sample spells in the core book. But since that's what we've got, I'm inclined to think its ok for creativity to stretch the boundaries of the guidelines.
As long as the result is something that is more limited, not more powerful, and no hermetic limits or technique/form guidelines are stretched or broken, while the story is enhanced, I really don't see a problem. Rules are there to facilitate storytelling, not the other way around. If I'm breaking RAW by contradicting it, that's bad (in how I run this saga) but if I'm just filling in fuzzy gray areas with a one-off case, that's ok I think.
Perhaps the unusual effect is why she was experimenting in the first place?
That makes it a combat usable weapon. Each round, you smack someone: They feel pain, lose a fatigue level. Or I have to remove the fatigue loss entirely, in which case, it doesn't have the desired effect of wearing out her unruly pupil (in story, this was an unintended, but benificial, side effect of the item invention).
Doesn't allow for longer torture sessions either, as after 6 rounds, they'd pass out.
Now, some might be thinking, why make an item at all? Why not just use a spell? She's, after all, a powerful magus. Answer: never risk botching in front of your pupil.
Some might wonder, why make the item so limited? The target needs to be bound or willing for the item to be useful. Answer: yep. Its a torture device, or something used on a "willing" target, like a pupil who must follow your commands, else suffer a worse punishment.
If she just wanted to kill the person, she's got Malfadeica for that