Let's throw another fly into the ointment of trying to define "incontinence" in the first place:
What about "functional incontinence", where you know you have to go, but simply can't reach a bathroom in time, maybe because you the bathroom is too far a way or you don't move very quickly anymore?
There are, as noted, various fairly well accepted adjectives to narrow down just what is meant by "incontinence"...such as urge incontinence or overflow incontinence.