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It doesn't sound like you have a chronic infection. Infections are usually treated with antibiotics (in this case, tobramycin). If the antibiotic is not effective (or the bacteria is resistant), then the infection would worsen. It would not keep recurring like this.
It sounds like you have a chronic inflammation. That is why the steroids helps, but when you are off the inflammation returns. There are many causes of chronic inflammation in the eye -- ranging from simple conditions like allergies, dry eyes to more severe conditions like sarcoidosis, episcleritis, scleritis, etc.
Sometimes, with inflammation, if you don't knock it down completely, it will linger and recur when the meds are off. You may need a stronger form of steroids to completely knock out the inflammation.
Hope this helps and thank you.