I've looked after a number of patients who've had both kidneys removed (because of cancer, polycystic disease and, in one case, by accident). Although any renal function is helpful, in terms of it exerting even a little influence over blood pressure maintainence, excretion, bone density etc, people without any renal function at all can still be effectively managed.
I can't speak specifically about your father's situation, both because it's against the Terms of Service to give advice and because (being neither a renal physician or having any knowledge of your father's condition) I don't know anything about him, his ciondition or his management. However, if the problem were related to bilateral nephrectomy (removal of both kidneys) it would show up almost immediately, not two years later.
It's not uncommon for people with renal failure, as with all chronic diseses, to have changes in their condition over time. Most often these changes are for the worse, as few chronic conditions resolve.
For the majority of my patients, a sudden change in their biochemistry (the 'toxins' removed in dialysis) usually means either that there's something else going on it their body, like another illness, or they've become less compliant with an aspect of their regime. The latter is much more common, and not surprising - it's really difficult to stick to the restrictive requirements of managing dialysis-dependent renal failure, particularly over time.
I hope this is of some help. If you or your father need support, a number of renal groups are available, depending what country you live in. To find some in your area type "renal (or kidney) support group" or "renal (or kidney) patient information" into google. I hope this helps.