... Selection of seed stock.
Although home growers hate to do this, (and so did I when I started out) I get really picky about which tubers I select for next seasons crop. I look for the larger ones that are well formed and have no blemishes. I pick the best for seed, not eating. But they are clones of the parent, you say? They shouldn't be any variations, you say? Well, we can say that over and over again, but Mother Nature actually allows for variation. The plant reacts to its environment, so even clones, like potatoes, can vary.
Back to selection. I use large tubers. The small, super jumbo, irregular, blemished one get eaten. Only the best are used for seed potatoes. On top of it, I also want to select from plants that are healthy looking, robust, and heavy producers of large tubers, not a few super jumbos or tons of little ones.
... Cull out diseased or weak plants. I know that there is the urge to grow out every plant, to get as many plants as possible. But this weaker plants are often diseased in some fashion, thus passing the problem to neighboring plants and infecting the soil. I'm quick to remove problem plants.
... Clean the seed potatoes prior to sowing. The seed potatoes go through a dormant period prior to sprouting. While in this dormancy, I remove any tuber that starts to show any problem. Plus I will give them a soak in a 10% bleach solution for ten minutes just prior to planting, letting them air dry.
... Keep the soil alive with fresh compost and nurture the soil organisms. Soil organisms can help a lot with keeping the garden healthy, suppressing pathogens (disease causing organisms). This is not a perfect solution, but it makes a positive difference. I've often heard that you shouldn't add fresh compost to potatoes, but heck, I've grown crops successfully in pure 100% compost.
... Change of location (aka- crop rotation). Again, not a perfect solution, but it can help. If one location shows signs of disease, then surely change to another. The problem with this is that gardeners tend to use the same tools on the entire garden area, thus spreading disease around. And many walk through their garden while the foliage is wet, again increases the chance of spreading disease.
Diminishing harvests, weaker plants, fading away are problems common to growing potatoes. When I see this happening regardless of my efforts, I bite the bullet and purchase fresh certified seed stock. While most gardeners see fading away after about 3 years, I don't buy fresh seed stock that frequently. So I guess my precautions help. I've only purchased certified seed stock 3 times since starting this farm.
The other part of the fading problem is soil fertility. Potatoes respond really well to fertile, evenly moist, light & fluffy soil. Yes, the big commercial farms grown potatoes in sand, clay, etc., but they use chemical fertilizers and aggressive hilling to compensate. Plus if yields fail below a certain level, farmers switch to another crop that is more profitable. On my own farm I've seen that if I fail to incorporate plenty of compost between crops, the potato harvest shrinks to less and less. They really respond favorably to fertilizer, be it commercial or homemade compost. Potatoes also seem to respond well to light soil. Light fluffy soil allows them to spread out roots better, making the plant larger and more robust...which translates into a bigger crop. I also like to keep the plants well mulched. My plants with a good mulch layer produce far better than the ones where I've skipped or scimped on mulch.
I find that certain varieties are more durable than others. Some yield better from the get-go, whiles others don't. Some "fade away" worse and faster than others. So part of the trick is to find the varieties that like your location and garden methods.