Depends on the type of antimatter you consider. Positrons and antiprotons can be stored for months in penning traps. I guess many years would be possible, but no one seems to bother keeping them that long.
Neutral antihydrogen is significantly harder to store, as it is not charged. The ALPHA experiment at CERN manages to store atoms for something like 15 minutes - probably more now but I didn't see anything new after 2011.
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