It does look like Asparagus wilt to me too. That is caused by a soil borne fungi. Since you have had the asparagus bed for a long time the disease will probably keep infecting a few more plants each year. You can dig down into the crown area underground if you want to be more certain to see if the crown/root area is getting a rot and weakening the stand. There really is no long term solution except to rotate out of the old stand to a new place with new material. Your stand sounds like it is still in pretty good health so you can try to dig out the worst area if you find some rotting roots.  

Thanks for your advice - it has "self-sown" into the far corners of the garden (near corner fenceposts where we don't rototill) so we will continue to enjoy it, and let it rotate itself to a new area, and dig up the infected plants.