Many trials are designed to collect outcomes at or around pre-specified times after randomization. In practice, there can be substantial variability in the times at which participants are actually assessed. As a result, treatment effects can be driven by the timing of assessments, rather than the effect of treatment on participants' underlying outcome trajectories. To avoid this problem, it is better to focus on the treatment effect at each of the (fixed) targeted assessment times. For this, untestable assumptions are needed. Therefore, it is important to assess how inferences would change under departures from these assumptions via sensitivity analysis. We develop such a sensitivity analysis methodology here, along with a semi-parametric, influence function-based estimation approach. We apply our method to a study of low-income participants with uncontrolled asthma, and we evaluate the performance of our procedure in a realistic simulation study. This is joint work with Bonnie Smith, Shu Yang and Andrea Apter.