- Strong growth in the 1990s
- A sharp disruption as a result of 9/11
- Even stronger rebound growth in the early 2000s
- An abrupt leveling off in 2005 with the onset of the plateau in oil production
- A decline with the great recession
- Weak growth since the end of the recession
I think this is more or less exactly what a peak oil moderate would have predicted. Air travel is an interesting case in that there's no way it's demand limited. Cars, for example, one might make a somewhat plausible case that further American demand for more vehicle-miles-traveled was going to be limited by already high car ownership and congestion and inability to fit more roads and parking into already crowded cities. However, it seems clear that, unconstrained by costs, many Americans would be jetting around every weekend for fun.
But jet travel is also something that does and will always depend on liquid fuel, so it is likely that constraints in the liquid fuel supply will directly show through into constraints in jet travel.
I would expect air travel to continue for a long time to come, but I also expect it to gradually become more expensive and less accessible to the bulk of the population.