Injectable medications are different from all other medications in terms of safety and stability.
Injectables medications are sterile because they are injected directly in to the body. Any microbial contamination can and sometimes do cause a serious infection if injected into a person. The safest injectable to use are the single dose products. Multi dose products that must be punctured time and again, risk the possibility of contamination each time a dose is withdrawn from the container. We try to minimize the possibility of contamination by using good technique, wash hands, wipe top of vial with alcohol, wipe injection site with alcohol.
It is true that multi dose vials contain a preservative, which does, most times, prevent microbial contamination from growing in the vial, but this is not 100% complete protection. Hospitals in the USA all limit the maximum stability of an injectable medication to 30 days, if kept refrigerated. The refrigeration almost completely stops the microbial growth, but the maximum limit is still 30 days after the vial is first punctured. You will see a date on each punctured multi dose vial, which is the date of the first puncture. If there is no date, it is assumed to be contaminated and discarded. Additionally, not all medications can be refrigerated.
For an injectable medication used at home, the manufacturer will print a package insert that will specifically spell out how long a punctured vial is good for and under what storage conditions. Read that package insert and take the recommendations as factual.
As always, consider the source of any recommendations.