The solution JLH successfully stored for years in the dark was not full of seed exudates, anyone who pre-soaks beans before cooking them knows seeds add stuff to the soaking water
Plant pathogens aside, my guess to the biggest problem would be the used solution rapidly growing bacteria and yeasts which could metabolize the GA3 or just make the solution unsafe to use (because the bacteria might eat your seeds). Even bleach pre-treating seeds wont stop that.
Freezing the used solution would stop any microbial growth and kill bacteria, probably increasing the number of times it could be used before going funky.
Another, probably lesser, consideration is that GA3 tends to be used on seed with hormonal dormancy, those dormins could get in the solution and at least partly counteract the anti-dormancy effect of GA3.
I've reused solutions but my preferred method is to make a potent GA3 tincture or stock solution (say, 0 to 20% alcohol) and dilute as needed to make very small batches of soaking solution. If you prefer a 500 ppm solution make a 1% solution and dilute 5 drops from a eye dropper or tincture style dropper bottle into 1 teaspoon of solution.