According to the concept of Ghosh (1982), a binary and connected block design D, with the smallest treatment replication r_[ν], is said to be maximally robust against the unavailability of data and with respect to the estimability of treatment contrasts, if a design D_#, obtained from D by deleting any r_[ν]−1 blocks, remains connected irrespective of the choice of the blocks deleted. Three sufficient conditions for the maximal robustness of a block design are derived. Their applications are shown in the context of certain variance-balanced block designs constructed by Kageyama (1976) and variance-and-efficiency-balanced block designs listed by Gupta and Jones (1983).