What's the longest time antimatter was able to be stored?
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.
More antiprotons ("no antiproton losses were detected over a period of several month")
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.
For pbars, I believe the record is 69 days, 10 hours, 18 minutes, from the Fermilab antiproton accumulator. This happened between 26 March 2004 and 4 June 2004.
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