I have found the expression “corte(s) de antigüedad” used in contexts where the sense of “corte” seems to be “cut-off" (date or figure), in other words, a threshold beyond which entitlements change. This example is from a Spanish trade union website:

“[...] Comisión de Selección de los cursos de Habilitación Funcional. [...] El corte de antigüedad ha quedado en 214 meses para Encargado General de Servicios, 101 para Ordenanza, 199 para Vigilante de Obras Públicas y 180 para Vigilante de Carretera.”
http://www.stas-clm.org/www/modules/news/article.php?storyid...

This must mean that the figures quoted are the minimum length of service candidates must have in order to take the various courses mentioned. Another example of this meaning, in a different context, is:
“La selección de galerías no se realizará por ningún tipo de corte de antigüedad de las mismas ni de edad de sus artistas, sino por la calidad de su trabajo”
http://www.feriade.com/feria_de_arte_contemporaneo_emergente...

However, in the present case this meaning doesn’t seem to fit. Instead, I think “corte de antigüedad” has the meaning suggested by the document DLyons cites in the discussion, where the “cortes de antigüedad” are “1 a 4 [años]”, “5 a 9”, 10 a 14”, and so on. In other words, bands. This meaning is closely related to that of a cut-off date: the “corte” or band is what lies between two cut-off dates, in effect. The idea of “corte” is really a slice, what might be called a tranche in the context of a loan. It is as if a continuum were cut into segments. It is rather similar to what is called a “tramo” in some contexts: a period of service entitling a worker to some benefit.

Here’s another example where the expression apparently refers to a band or period, though in a different context:
“Tabla 12
Resolución de expedientes pendientes en los dos primeros años de gobierno de Cárdenas por corte de antigüedad”
Figures are given for “expedientes antiguos” and “expedientes nuevos”.
http://books.google.es/books?id=vgQsKwYAaZgC&pg=PA179&lpg=PA...

The equivalent expression in English is “length-of-service band”, which can be readily found used in the same way. For example:

“To set up length of service bands for a PTO plan:
1. For each length of service band applicable to this plan, establish the band's duration by making an entry in the To field. The first band starts from zero years of service. If it extends for five years, enter 5 in the To field. The system then sets the From field for the second band at 5, as the second band starts after five years of service.
2. For the last band you enter, in order to cover all participants with any length of service beyond the band's From entry, enter 99 in the To field. For example, if your bands cover service of 0-5 years, 5-10 years and 10+ years, the third band's From and To entries should be 10 and 99.”
http://download.oracle.com/docs/cd/A60725_05/html/comnls/us/...

I think “length of service” would be better than “seniority” for “antigüedad”, because “seniority” tends to imply some promotion or performance-related element, whereas what seems to be involved here is simply how many years a person has worked.

What is slightly puzzling is that it says “cortes”, plural, though it apparently refers to one employee. I presume the sense may be how many periods of X years have been completed, in the same sort of way that people in certain professions can have accrued a number of “tramos” or “quinquenios” or “sexenios”, which bring them salary increases.

You can word it however you like.

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Note added at 12 hrs (2011-03-03 09:34:13 GMT)
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Note: "corte" may refer to breaks/gaps/cutoff points in the period calculated.
DRAE: corte: Terminación que, sin anuencia del acreedor, da a las cuentas.

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Note added at 12 hrs (2011-03-03 09:36:22 GMT)
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Baasic concept: there is an allowance for the numbers of years worked. The allowance will be docked in line with any interruptions to this period.

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Note added at 12 hrs (2011-03-03 09:39:35 GMT)
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See entry by Charles for more in-depth references.