For months, see
this information page, which summarises Australian research and states, "When cell-associated, the virus may survive for months in poultry house litter or dust and is resistant to
some disinfectants." (My emphasis).
This is why a disinfectant that is effective on Marek's is required.
For a long time in dry environments (Adelaide is the driest capital city on the driest continent, except for Antarctica which is technically a desert with no rain). See
this paper.
It's not gone.
But the chickens don't have it at this time.
Do you know of any studies providing evidence that environmentally friendly soap is effective against the Marek's virus? If so, I'd love to read them!