Continuous effect

Some cards have the [永] symbol beside their effect. Does this [永] effect apply during your opponent's turn or only during yours?

E.g. Asura Kaiser, rearguards all gone during opponent's turn. Does Asura Kaiser drop to 9000 power or remain at 11000? It's [永] effect says if it has no other (Nova Grappler) units on his side of the field, it's power is reduced by 2000.

It checks all the time. For Asura Kaiser's case.