To the extent average utilitarianism is motivated by avoiding the Repugnant Conclusion, I suspect that most average utilitarians would be as disturbed by aggregating over time as they are by aggregating within a generation, since we can establish a Repugnant Conclusion over times pretty straightforwardly. That said, to the extent intuitions differ when we aggregate over times, I can see that this could pose a challenge to average utilitarians.

I can't recall any work on this argument off the top of my head, but I did recently come across a hint of a related argument directed against distributive egalitarianism. From https://globalprioritiesinstitute.org/economic-inequality-and-the-long-term-future-andreas-t-schmidt-university-of-groningen-and-daan-juijn-ce-delft/ : "An additional question is whether distributive egalitarianism should extend to inequalities across generations." Which links to a footnote: "One of us elsewhere argues that distributive egalitarianism is implausible, because its extension to intergenerational distributions is necessary yet implausible [redacted]." Not sure why the citation is redacted, but I think "one of us" refers to Andreas Schmidt. Of course, extending the analysis to future generations threatens average utilitarianism and distributive egalitarianism in different ways. But the fact that both are threatened by this type of argument suggests to me that a lot of moral theories ought to be stress-tested against "what about across generations?" arguments. I agree that there's an interesting set of questions here.