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.
http://gabrielse.physics.harvard.edu/gabrielse/papers/1994/1994_haarsma/chapter1.pdf Positrons 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.