Oh, I've always wanted something along these lines. I've yet to find an app that handles "this thing, if I'm late, still needs to be on-time next time" (like a mortgage payment) versus "this thing, if I'm late, should move all future occurrences accordingly" (like cleaning the toilets).
Gonna pile on to other's suggestions, and say Todoist can do this. You can schedule a task to happen every four weeks, and the next occurrence happen four weeks after you complete it (even if you're a few days late) or four weeks from when it was last due. Pretty nice for my needs, might fit yours too.
I use an app called 'Alarmed' on my iPhone for this. It's got everything I need, in particular you can repeat items on a fixed period or 'x days from the time you actually manage to tick it off', which is great. It's free with a one-off IAP to unlock extra features (can't remember what they are - I paid it years ago).
Omnifocus has repeatable tasks and you can pick whether they repeat based on the due date (once a month, like the mortgage), or on completion date (I use this for cleaning chores, so if I'm late to clean the bathroom, don't tell me to do it in 2 days because it's Saturday, tell me to do it 1 week from now)
It does, as does Todoist and other task managers. But it's never a first class citizen and takes a backseat to one-off task management. For many, these features or even Google Sheets or the Notes app is sufficient. It wasn't for me, though.
