Achievable data rates in wireless systems rely heavily on the available channel state information (CSI) throughout the network. However, feedback links, which provide this information, are scarce, unreliable, and subject to security threats. In this work, we study the impact of having intermittent feedback links on the capacity region of the canonical two-user erasure broadcast channels. In our model, at any time instant, each receiver broadcasts its CSI, and at any other node, this information either becomes available with unit delay or gets erased. For this setting, we develop a new set of outer bounds to capture the intermittent nature of the feedback links. These outer bounds depend on the probability that the CSI from both receivers are erased at the transmitter. In particular, if at any time, the CSI from at least one of the two receivers is available at the other two nodes, then the outer-bounds match the capacity with global delayed CSI. We also provide capacity-achieving transmission strategies under certain scenarios, and we establish a connection between this problem and Blind Index Coding with feedback.