I would think that storing it sealed and frozen would be the best way to keep it fresh. As long as it's under refrigeration, spoilage shouldn't be an issue, but I know volatile aromatics will still escape over time.
Liquid malt syrup is easy to store as long as it is in the original can. This is an ideal container that keeps the syrup safe from light and oxygen, and the malt is good for about two years before it starts to degrade. The manufacturer has normally also heated the syrup to pasteurize it before shipping, so it is void of bacteria, molds and yeast. Most cans have an expiration date that helps you know when it is getting old. The same temperature range (50¡ to 70¡ F) applies.
Liquid malt syrup that has been opened, or is sold in bulk plastic containers, has a much shorter shelf life. While buying malt syrup in this form is normally less expensive, it must be used in less than 3 months, or the syrup will degrade or even grow mold. If you have malt syrup in this form, the best way to store it is in the fridge. Pick the smallest possible container to eliminate airspace and avoid oxidation. While the extremely high sugar content inhibits yeast activity and molding, over a three- to four-month time period the syrup will lose its freshness.
Really though, outside of a month or two, staling and darkening are inevitable, regardless of the storage method. Overbuying LME is not recommended.