At least 12 years apparently!
Twin delivery following 12 years of human embryo cryopreservation: Case report
In mice, stored embryos have been successfully resuscitated after 20 years of storage in liquid nitrogen, and cow sperm has been viable after 37 years of storage. Although it's impossible to test much further than that currently, it's predicted that they should remain viable almost indefinitely. This does raise ethical concerns for some people, especially if they believe life begins at conception.
This of course depends on a few things:
An available source of liquid nitrogen. Storage tanks are 'leaky' by design and have to be topped up regularly
Radiation. A study showed that mouse embryos can survive at least 2000 years of background radiation, but if that level is much higher (eg nuclear war etc) then they would need to be protected.
Cost. Storing embryos is really expensive, and freezing plus proper resuscitation is a highly skilled job