Number of successes is intended to be constant
The Exploit Raise Dead says it's an Extended Action.
Extended Actions are detailed in DtD, page 312-314. The way they function is that the number of rolls is defined, then the number of successes is defined, and time between rolls. Then the dice come out.
Increasing the number of successes is not a standard step, and the text of the Exploit doesn't deliberately include it, so, in adhering to description of an Extended Action, it's not intended to be enforced.
In other words, if you need 13 successes on day 1, and roll 4; the next day, you still need 13 successes (but have 4 "in the bank")
Now, the compliment to this is that, upon a failed roll during an extended action, the character gains a negative Condition (or abandons the attempt). On page 313, it even suggests a Condition of "Frustrated", which doesn't exist in the official Conditions list.
As such, an example Condition that may be appropriate might be:
While performing Raise Dead, your character has lost focus on the Exploit enough to cause a disruption. Perhaps the body resumes decaying; perhaps the soul has become lost.
Add the number of rolls already attempted to the target success number.
Resolution: Gain a beat, or end the Exploit
Beat: Your character brings the Exploit "back on track" via rolling an Exceptional Success