Take a look here:
http://www.largeformatphotography.info/fstop.html and pay attention to the section on storage life of the working solution.
Even though this is for an Ilford product (which I use and recommend), It applies generally to most similarly-formulated rapid fixers (i.e., slightly acidic)
Then, do your best to NOT store your fixer working solution longer than the recommendation for the container you are using (e.g., full, tightly-capped bottle, or half-full bottle, etc.). If you can do that and your storage conditions are good, you'll eliminate your sulfurization problem.
As for the bottle, I'd probably just toss it and start over and chalk up the $5 to tuition for HKU (Hard Knocks University).
FWIW, I try to only mix enough fixer working solution for the amount of film I'm developing at a particular time. If you're shooting roll film, you don't need to mix a liter, or 500ml even, just enough for the tank you are using. If you've saved up enough rolls for a batch of fixer, then you can just discard it after use, eliminating the entire storage scenario and the uncertainties that go along with it. If you do end up storing working solution, try to use a good bottle filled to the brim and tightly capped. This will give you the best storage life.
Finally, don't exceed the capacity of your fix. Use the throughput guidelines or, better, do a clip test before each batch. When the clearing time is 2x that in fresh fixer, discard your fix.
Best,
Doremus