GOSH!!!! you have asked the million dollar question which has no answer. its soooo different for each mama-child combo.
so here is my story. when i got pregnant i said come hail or highwater nothing was going to stop me from nursing my child. but i never had a number figure in my head. i had this idea of CLW but not the age. so when dd turned one i remember being surprised that i had carried on so long (lots of stuff happening in life along with WOH pumping). then 2 came and i was still surprised. by 4 i wasnt anymore. but if you told me that when i was pregnant that i would be nursing a 6 1/2 year old with no end in sight i would have told you GAH!!! no way!!! i would never have thought i could last that long.
my dd 6 1/2 nurses when she is with me which is every alternate weeknights and weekends - for about 30 - 60 secs before falling asleep (we still cosleep

). if for whatever reason my nipples are sore and i say no she is fine with it. once in a while she will nurse in teh am too upon wake up for 30-60 secs.
my milk dried up when she was almost 3. i find after 4 her intensity to nurse goes thru phases. when she is under stress - by which i mean going thru an emotional tough time - then she HAS to nurse even for that 30-60 secs. otherwise some nights (which is not that often) she doesnt ask to nurse.
i never offer. i dont really think i ever have after she was a baby.
at any time of the day seh still cant resist a naked boob. she quickly takes a couple seconds 'nursing'.
btw i have always enjoyed our nursing relationship and still do.