Maybe a thorough treatment against mould is in order?
From google I pulled up two links here and here that could point to the problem being a type of white mould
The first link talks about the problem on a popular composite deck surface but the second appears to talk about it on wooden surfaces including the construction underneath. Â
Have the seen the underneath of the deck lately? Could there be a problem with ventilation underneath the deck or a nearby waste water source for the spores to take hold from?
Good luck solving it in any case and please keep us posted