The Oxford DNB article about this Beauchamp family states, [1]
[Robert de Beauchamp's] elder son, Miles de Beauchamp (d. 1142x53), tried unsuccessfully to turn Stephen's problems to his advantage, promising to support Stephen if he did not try to remove him from Bedford Castle, but he was forced out after a siege at Christmas 1137. In 1141 Miles and his followers recovered the castle, 'as triumphant and fierce as they had once been humble and downcast' (Gesta Stephani, 33), only to lose it once again before both barony and castle were returned to the Beauchamps by Henry II.
[1] Kathryn Faulkner, "Beauchamp, de, family (per. c.1080–c.1265)," Oxford Dictionary of National Biography (Oxford University Press, 2004, online edition), [Oxford_Dictionary_National_Biography], [OxfordDNB(UM)].