Do Spirit races persist in decline indefinitely?
Yes they will stay on the board because the spirit power overrides the rule that prevents them from being removed while in decline. The White Ladies are unlikely to have a lot of territory as other players are likely to target them strongly before you have a chance to put them in decline.
https://www.ultraboardgames.com/smallworld/special-powers.php

When the race tokens associated with your Spirit Special Power go into Decline, they never count toward the limit stated in Entering In Decline regarding having a single In Decline race on the map at any given time.