Preserving the connectivity of the underlying interaction graph in a multi-robot system is a necessary condition for allowing the group of robots to achieve a common task by resorting to only local information. However, in the context of open multi-robot systems, that is, when the number of robots in the team is not fixed, merely preserving connectivity of the current graph does not prevent the loss of connectivity after a robot joins/leaves the group. We present a distributed strategy to achieve biconnectivity, instead of simple connectivity, for a group of robots that allows establishment/deletion of interaction links as well as addition/removal of agents at anytime while guaranteeing that the connectivity, and thus functionality, of the team is always preserved. The proposed approach is completely distributed and embeds into a unique gradient-based control multiple constraints and requirements: (i) limited inter-robot communication ranges, (ii) limited field of view, (iii) desired inter-agent distances, and (iv) collision avoidance. Numerical simulations illustrate the effectiveness of our approach.