With the service-oriented encapsulation of Internet of Things (IoT) devices, IoT services, which are functionally compatible and non-functionally satisfiable, are composed to support domain applications. The execution of IoT services may last for a relatively long time duration in which their capacities may vary significantly. In this setting, whether or not, and to what extent, certain constraints specified upon certain IoT services can always be satisfied during their execution, are to be explored. This observation motivates us to formalize the interpretation of qualitative and quantitative satisfaction for prescribed constraints, and thus, to conduct IoT service monitoring at runtime. Specifically, the requirement of IoT service monitoring is formulated as a constraint satisfaction problem. Specification-based monitoring is developed leveraging Signal Temporal Logic (STL), where a novel accumulative robustness metric, denoted Accumulative STL (ASTL), is proposed to emphasize the robust satisfaction over the entire time domain. Hence, an ASTL-based mechanism is proposed to support IoT service monitoring, where prescribed constraints are converted to ASTL formulae, and interpreted with qualitative and quantitative semantics at runtime. Case studies and extensive evaluations are conducted upon publicly-available datasets. Experimental results show that ASTL performs better than the state-of-the-art techniques with more robust satisfaction.