Its good that you were rotating the crops (ideally potatoes should only be grown in the same spot every 3-4 years), but you might be right about soil depletion as potatoes are very heavy feeders. Also is the soil was left bare at any stage after harvesting, rain and sun will deplete the nutrients further - in this case weeds are actually better than bare soil:)
Digging also destroys the soil structure and leads to nutrient loss, so converting to ’no dig’ gardening methods, and putting in cover crops each winter might be an idea too.
There are places you can send soil away for testing if you’d like, but looking at what weeds did spring up is another way to identify deficiencies e.g. clover indicates low nitrogen, creeping buttercup may indicate soil compaction, dock leaves may indicate low calcium and high magnesium, potassium, phosphorus. Living locally ourselves, we’ve found through soil testing that land which has had cattle on it previously (even if many years ago) tends to have nutrient imbalances.
Adding a thick layer of well rotted organic horse manure or compost (bought or homemade) should give the soil a good boost and provide nutrients for the potatoes, and putting a mulch on top will also minimise weeds and replenish the soil over time. There are also organic plant foods you can buy which are concentrated versions of seaweed to condition the soil quickly. We do have a new product, Hexafrass which we are excited to try ourselves this year, it’s pre-charged with microbial colonies that slowly release nitrogen over time.
Do you have any tips to share with Padraic & Bridie?