Personally i wouldn't say that failing a secondary objective would cause the primary objective to be failed.
while secondary objectives can be important they are after all secondary, at most failing them should make it harder to complete the primary. if you are feeling particularly cruel it could make it almost impossible to pull off but there should still be a chance to complete.
for example if the primary mission was to destroy a facility and one of the secondary objectives was to convince an adeptus mechanicus techpriest to leave their post for a time.
if the secondary is completed then the techpriest wouldn't be there to stop critical systems from being broken (or raise the alarm over them being broken)
if the secondary was failed then the techpriest may implement additional checks or even organise more guards in the critical locations .
i wouldn't mean the primary objective was failed but it would make it a lot harder to complete.