Why is Kimbolton School's motto 'spes durat avorum'?

The following explains how the motto: SPES DURAT AVORUM [Alternatively, translated as:The hope of my ancestors continues, or Let the hopes of our forefathers endure, or May the hope of our forefathers endure, or The hope of my ancestors endures] became at some point in time associated with Kimbolton Castle.

The motto: SPES DURAT AVORUM is associated with Frederick Nassau de Zuylestein, third Earl of Rochford (1683/1684-1738) who was married to Lady Bessy Savage (1699-1746) an illegitimate daughter of Richard Savage, fourth Earl Rivers (c. 1660-1712). The first Earl Rivers was Richard Wydevill (1405-1469) married to Jacquetta de Luxembourg (1415/1416-1472). Their daughter, Katherine Woodville (c. 1458-1497), was married to Richard Wingfield of Kimbolton Castle (c. 1456-1525).

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The motto Spes Durat Avorum is also the motto of Queen Elizabeth High School(QEHS), Hexham, Northhumberland, NE463JB, England, established in 1599.

The following is the school's song:

Spes Durat Avorum

Hope of our sires, O live on eternally

Gleam yet more brightly the older you grow.

Send forth your children and watch them maternally

Keeping the spirit of kinship aglow.

Long may you flourish and prosper exceedingly

Lighting the future with torch of the past;

Ever may trouble pass by you unheedingly:

Long may the hope of our ancestors last!