When using column generation, can a sub-problem be ignored once and for all once it fails to generate a new column?

Suppose you are solving a minimization problem with a column generation procedure, and that you have $$2$$ sub-problems. At some point, one of the $$2$$ sub-problems is no longer able to generate a column with negative reduced cost.

Does this sub-problem never have to be solved again ? Or is it possible that a few iterations later, given the interaction with new columns from the other sub-problem, it is possible that a new column may be found ?

Thanks !