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.