Another approach would be to allow relative dates on yearly, quarterly, and biannual tasks. For example, "every 1 year on may 1" or quarterly tasks such as "every 3 months on the 15th". Then if the first occurrence is changed, the next should still be May 1. I would love this type of functionality because yearly tasks are often hard to pin a good due date on, so when they pop up I'm always changing their due date.

Thanks to a suggestion from support, I've been able to work around this for my monthly tasks by using things like "every month on the 1st" which causes subsequent repeating tasks to always land on that specific day of the month regardless of when the original has been postponed to.

However, as Jeff points out, for yearly tasks, this is a bit more complex. What's really odd however is that syntax like "Every year on the 1st Sunday in May" would work just fine, yet "Every year on May 1st" does not. The fact that the more complex condition would work over the simpler one has me scratching my head, but it might be a viable workaround for some situations until a better option comes around.

Something that looks relatively easy to do and very helpful would be, for repeating tasks, to add a "next occurrence" ("next" for short) that displays the date after the current occurrence is completed. This way, one would notice there may be something wrong with the repeat date and provide an opportunity to fix
it before it's too late.

When the due date for a task arrives, the next instance is generated. If you only postpone after that, the next instance's date will not change.
I often postpone "every year" tasks (especially for birthday presents ;-)) and everything works as expected. Just avoid postponing before the task is due. :)

I always use Start Dates for tasks of that sort. I set the Due Date as a deadline, so to speak, and then I set the Start Date to whatever date I want it to show up on my radar. I can then complete it or ignore it until I'm ready to deal with it.