Under normal circumstances, a Shadow doesn't have to roll in order for a Thorn to work. The Thorn activates once the Shadow pays the Tainted Essence required, and stays on either for a scene or for however long it takes for the Thorn to take effect. Once the time runs out, the Shadow can continue the Thorn's effects by paying Tainted Essence, again, or choose to let it go away.

Extended Play

Shadows may attempt to radically increase the time period of a Thorn. This requires a roll, and costs more Tainted Essence to attempt, but if it works the Shadow can delude, confuse and alienate the Wraith for much longer than normal. This goes a long way towards the Shadow's goal of getting its Wraith Lost.
 
In order to do this, the Shadow decides what it wants to have the Thorn do, and spends three times the normal cost to activate the power. It then rolls Permanent Willpower + Angst against the Wraith's Permanent Willpower + Eidolon in a Contested Roll. Each Success scored over Wraith's total keeps the Thorn active for a day and a night, doubled with each success after the first. An Exceptional Success keeps the Thorn going for a lunar month.

Cost: 3X normal for the Thorn
 
Dice Pool:  Resolve + Composure + Angst vs. Resolve + Composure + Eidolon
 
Action:  Contested
 
Dramatic Failure: N/A
 
Success/Failure:
 
If the Shadow fails, nothing happens - the Thorn doesn't even go off as normal, and it has wasted its Tainted Essence

If the Wraith fails, the Shadow succeeds and the Thorn is active for a day and a night for the first success, doubled for each success thereafter. {One success = one day & night, Two successes = two days & nights, Three successes = four days & nights, etc.}
 
Exceptional Success:
 
An exceptional success for the Shadow gets the Thorn going for lunar month.