Low-power wide-area network technologies such as LoRaWAN are promising for collecting low-rate monitoring data from geographically distributed sensors, in which timestamping the sensor data is a critical system function. This paper considers a synchronization-free approach to timestamping LoRaWAN uplink data based on signal arrival time at the gateway, which well matches LoRaWAN's one-hop star topology and releases bandwidth from transmitting timestamps and synchronizing end devices' clocks at all times. However, we show that this approach is susceptible to a {\em frame delay attack} consisting of malicious frame collision and delayed replay. Real experiments show that the attack can affect the end devices in large areas up to about $50,000\,\text{m}^2$. In a broader sense, the attack threatens any system functions requiring timely deliveries of LoRaWAN frames. To address this threat, we propose a $\mathsf{LoRaTS}$ gateway design that integrates a commodity LoRaWAN gateway and a low-power software-defined radio receiver to track the inherent frequency biases of the end devices. Based on an analytic model of LoRa's chirp spread spectrum modulation, we develop signal processing algorithms to estimate the frequency biases with high accuracy beyond that achieved by LoRa's default demodulation. The accurate frequency bias tracking capability enables the detection of the attack that introduces additional frequency biases. We also investigate and implement a more crafty attack that uses advanced radio apparatuses to eliminate the frequency biases. To address this crafty attack, we propose a pseudorandom interval hopping scheme to enhance our frequency bias tracking approach. Extensive experiments show the effectiveness of our approach in deployments with real affecting factors such as temperature variations.