https://en.wikipedia.org/wiki/Electrical_discharge_machining
Wikipedia
A wire-cut EDM machine using the CNC drawing plotter and optical line follower ... Also, applications of this process to shape polycrystalline diamond tools have ...

It is obviously an EDM-machine (Electric Discharge Machning), in Spanish “mecanizado por descarga eléctrica”, also known as “electroerosión”. In this specific case, the cutting/processing of the piece is achieved by means of a wire EDM. If I am right, “plano de vida” might then refer in this context to the specified wire inclination or orientation (= wire angle in relation with the programmed movement) that is specified by the machine operator (see definition in the link below) to process the piece and give it a specific shape (perhaps a conical shape???).


https://docs.google.com/viewerng/viewer?url=http://server2.d...
Manual de manejo y operaciones de la EDM ONA PRIMA -250

3.4.- CORTE CÓNICO
En este tipo de corte el hilo se inclina un cierto ángulo respecto a la posición de verticalidad, con objeto de dotar a la pieza de conicidad, imitando la forma geométrica definida en la otra cara, para ello es necesario especificar el espesor de la pieza, la posición de la guía superior y la altura respecto del plano principal de un plano de vida.
El plano de vida es donde se origina la inclinación del hilo sobre la trayectoria programada.
(…)

http://www.onaedm.com/gestor/recursos/uploads/archivos/ONA_T...
Maximum angle of conical cut

http://www.onaedm.com/en/productos-3/ona-af25-4


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Note added at 8 hrs (2016-03-05 19:58:09 GMT)
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This reference describes the die-stamping process. According to this information, “plano de vida” of a piece would be the side of the die where (in your case) a wire processes the piece shaping it. The wire is then responsible for shaping the part until the piece attains its final shape. The inclination of the wire (angle) and other parameters are determined prior to the beginnnig of the processing operation. This means that my initial interpretation was not fully correct. My confidence level is middle now, as it was before.

http://myslide.es/documents/matriz-solidworks.html

En este ensamblaje se parte de una pieza rectangular, que será la hembra de la matriz, con una anchura mayor que la banda y con una longitud aproximadamente igual a la banda. En cualquier caso, estas medidas podrán ser editadas y modificadas con facilidad si el diseño lo requiere. A continuación se generan los huecos de corte haciendo un trazado equidistante al contorno con una separación correspondiente a la mitad del juego previsto entre punzón y matriz. Para la determinación del juego de corte hay que recurrir de nuevo a la experiencia o a fuentes bibliográficas contrastadas [15]. Seguidamente, se debe generar el plano de vida de la hembra, esto es, un espesor útil en la matriz para compensar las operaciones de rectificado de la matriz como consecuencia del afilado de la misma.

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Note added at 7 days (2016-03-12 22:14:20 GMT)
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Matt, thank you for your update. It´s really a pity that you received so little feedback from your client. "Program plane" means actually nothing to me, probably as little as it means to you. Meantime I´m quite certain that your "plano de vida" corresponds to the area of the piece that is about to be processed or shaped (therefore "vida"/"área viva" = area to be shaped). This use seems to be metaphorical.

Thanks again. Toni.

the life time of something