A self-sealing valve comprises a valve housing having a fluid conduit, a valve seat, a diaphragm and a support member. The valve housing is configured to pass fluid through the fluid conduit. The diaphragm provides a self-seal of the fluid conduit. The support member is configured to retain a portion of a diaphragm. The support member and diaphragm are configured to position the flexible diaphragm against the valve seat to seal the fluid conduit in a closed position of the self-sealing valve, and to facilitate movement of the diaphragm under a bias in a first direction away from the valve seat to an open position.