In some embodiments, an apparatus includes a module within a first stage of a switch fabric, a module within a second stage of the switch fabric, and a module within a third stage of the switch fabric. The module within the first stage is configured to send data to the module within the second stage. The module within the second stage is configured to send data to the module within the third stage. The module within the second stage is configured to send a first suspension indicator to the module within the third stage. The module within the third stage is configured to send a second suspension indicator to the module within the first stage in response to the first suspension indicator. The module within the first stage is configured to stop sending data to the module within the second stage in response to the second suspension indicator.