Data aggregation scheduling, or convergecast, is a fundamental pattern of communication in wireless sensor networks (WSNs), where sensor nodes aggregate and relay data to a sink node. For WSN applications that require fast response time, it is imperative that the data reaches the sink as fast as possible. For such timeliness guarantees, TDMA-based scheduling can be used to assign time slots to nodes in which they can transmit messages. However, any slot assignment approach needs to be cognisant of the fact that crash failures can occur (e.g., due to battery exhaustion, defective hardware). In this paper, we study the design of such data aggregation scheduling (convergecast) protocols. We make the following contributions: (i) we identify a necessary condition to solve the convergecast problem, (ii) we introduce two versions of the convergecast problem, namely (a) a strong version, and (b) a weak version , (iii) we show that the strong convergecast problem cannot be solved, (iv) we show ...