Complete measurements, while providing maximal information gain, result in destruction of the shared entanglement. In the standard teleportation scheme, the sender's measurement on the shared entangled state between the sender and the receiver has that consequence. We propose here a teleportation scheme involving weak measurements which can sustain entanglement up to a certain level so that the reusability of the shared resource state for reattempting teleportation is possible. The measurements are chosen in such a way that it is weak enough to retain entanglement and hence can be reused for quantum tasks, yet adequately strong to ensure quantum advantage in the protocol. In this scenario, we report that at most six sender-receiver duos can reuse the state for reattempting teleportation, when the initial shared state is entangled in a finite neighborhood of the maximally entangled state and for a suitable choice of weak measurements. However, we observe that the reattempt number decreases with the decrease in the entanglement of the initial shared state. Among the weakening strategies studied, Bell measurement admixed with white noise performs better than any other low-rank weak measurements in this situation.