My mom had a strawberry patch for many years and never moved it. As the years went on she got less and less berries and they got smaller and smaller too.
This is my 4th year growing strawberries and I have moved them to a new spot. I probably could have (and kind of wish I would have) kept them going in the same spot at least another year, they were still giving me lots of big berries. I don't use any kind of herbicides or anything like that on them though, and they were really starting to get overgrown with weeds. It's difficult, for me anyway, to keep strawberries well weeded. It was more for that reason than anything that I moved them. I pulled up everything I could and then covered the area with black plastic to kill all of the weeds. This spring I tilled in lots of compost and we've been piling all of our lawn clippings onto that spot to keep the weeds down. We'll just let the clippings compost down into the soil. Hopefully by the time this new patch is done, we'll be able to replant in the old area again with the soil rejuvenated.