I do 'rejuvenate' the soil in my Earth Boxes before re-planting each fall. I take out maybe the top 4in. of potting mix and old roots, douse the whole thing with 1% hydrogen peroxide to guard against any bacterial blights that might be lurking. Then mix in some alfalfa pellets to the soil that's left and add a new strip of fresh fert before re-filling with fresh potting mix. The tomatoes in my Earth Boxes absolutely jump up, and get really huge, so they're heavy feeders.
About every second year I completely empty the boxes, clean them up and start fresh. Use the old potting mix as soil amendment in the flower beds, though so it doesn't go to waste.
If you're careful, you can probably work around that little volunteer, though. Can't deny a plant that resilient!
Btw, I don't think you actually had "failures" this summer. Heck, that plant was still alive, obviously. There's another factor that inhibits growing tomatoes here - when the night temperatures don't get cool enough in summer, even if the plants are still healthy, the flowers won't set fruit on most varieties.
I tried a couple of "heat tolerant" types last spring and they were no better than the regular tomatoes. They all stopped at once, about the middle of May. It really DID get hot awfully early this year. Usually they at least make it into June.
