Wow! Fifty-four years ago from seed? That is incredible! So here are some things you can do to prevent spider mites:
CANOLA OIL SPRAY RECIPE
Mix 1 part canola oil into 50 parts water (approximately 1 tablespoon oil to 1 liter water). Add a few drops of dish detergent and shake well. Spray tops and bottoms of leaves and stems generously. Test in a small area first.
Other homemade sprays you could try (again, I haven't used these myself) include garlic, basil, coriander, chive spray, feverfew, or dill spray (make a strong tea with the leaves (or crushed garlic, and use within a few days). Please, please, please test in a small area first before covering your whole tree.
You can also try a pyrethrum dust. Keep in mind that all of these chemical solutions (although the least toxic of your options) should not be used indoors. They are also better when applied in cooler weather or they may cause leaf scorching.
As always, keep all chemicals and home remedies away from pets and children.
Not a plant expert at all but check out the info on these links. Isolate the plant...try the soap or the iso alcohol treatment... and the raising the humidity sections. Seems like my parents used to mist their plants with water to keep the spider mites away. That is such a long time to have a plant and from a seed no less. It would be a shame not to save it. Good Luck!
Though spider mites are not true insects, it still might work to use diatomaceous earth. Use garden quality, it is organic and won't harm humans or pets. Since it is a dust, just be careful not to breath in much of it or get it into your eyes. Check out TheGardenGuy.com for organic solutions. He created a gorgeous garden on part of a parking lot at the Channel 3 TV Station here in Phoenix and is a regular on their shows. Guest chefs often cook out there too. I have both his books on Southwest gardening.
Pepper Spray is an organic and safe insecticide which will take care of spider mites very well. Sold in the home gardening section of your home improvement stores.