It depends on drainage. In my very sandy, very poor soil, I better add
something new every year. In clay soil, nutrients may be better
retained. Compost is still good in the second or third year, as far as
humus and water retention. So a little fertilizer will make it as good
as new. Do not overestimate the nutrient content.

Some numbers: compost may have 0.2-0.3% P and K by dry weight if
prepared with yard clippings. One ton of wet compost may then have some
2 lbs of K. Those 2lbs are just what I get from 25 tomato plants and
maybe 8 squash plants in one year. And that is not including that most
K leaches into the subsoil and that in october I throw away the plants
to limit disease. Herbivory can deplete your soil faster than you
think, specially with K and fruiting veggies. Of course I add much more
than one ton of compost, and I also add tens of pounds of wood ash. I
add some phosphate (some P is in the ash, and all micronutrients are in
there as well except S), but much less because P does not leach. N
comes from a variety of sources such as manure and kitchen scraps in
the compost, grass clippings used for mulch, beans crops, blood meal
to discourage rodents, etc.