Even one warning during an approach is bad enough and suggests that a go-around would be a good idea.
Multiple warnings would surely remove any doubt about continuing to land and are best prioritised and delalt with once a safe flight path has been established and the missed approach procedure complied with.
Fear of loss of face from going around may well have played a part, culturally it may only be acceptable for the senior pilot to decide whether to continue, and unsolicited advice from a junior would be regarded unfavourably. When CRM is really bad it might even cause the senior pilot to feel he has to prove a point and establish his authority.
With engine bypass ratios becoming higher and ground clearance being reduced, has adequate consideration gone into the location of vital components such as pumps, gearbox’s and supply lines ? Whilst space is obviously constrained, having vital systems in a vulnerable position should be avoided.