Consider an energy harvesting node where generation of a status update message takes non-negligible time due to sensing, computing and analytics operations performed before making update transmissions. The node has to harmonize its (re)transmission strategy with the sensing/computing. We call this general set of problems intermittent status updating. In this paper, we consider intermittent status updating through non-preemptive sensing/computing (S/C) and transmission (Tx) operations, each costing a single energy recharge of the node, through an erasure channel with (a) perfect channel feedback and (b) no channel feedback. The S/C time for each update is independent with a general distribution. The Tx queue has a single data buffer to save the latest packet generated after the S/C operation and a single transmitter where transmission time is deterministic. Once energy is harvested, the node has to decide whether to activate S/C to generate a new update or to (re)send the existing update (if any) to the receiver. We prove that when feedback is available average peak age of information (AoI) at the receiver is minimized by a threshold-based policy that allows only young packets to be (re)sent or else generates a new update. We additionally propose window based and probabilistic retransmission schemes for both cases (a) and (b) and obtain closed form average peak AoI expressions. Our numerical results show average peak AoI performance comparisons and improvements.