Offhand I'm not sure which statute would apply, but if there is none, then the "catch-all" 4-year statute applies. However, if he resigned (and this is documented somehow), he probably didn't have the authority to do anything with the corporation anyway, which may be another way to challenge the dissolution.

Without doing research in such depth I'd have to charge for it, I'm gonna guess that when the last director resigns with no replacement, said last director's resignation is either ineffective or can be retracted, or that he remains in office until a successor is appointed by those with power to do so, or by a court. It is within a court's power to break corporate stalemates by appointing provisional directors. See e.g. Corporations Code section 8512.

Note also CC 8711 providing that a vacancy on the board during winding up of an NPMBC may be filled in the manner provided in CC 7224.

As to statutes of limitations:

Corporations Code 7527 sets a nin-month limit on filing actions to challenge any election, appointment or removal of a director of an NPMBC. This might apply.

CC 8618 sets additional barriers to suits against NPMBC's that are winding up. Finally, see Corporations Code 8723 for a lengthy and broad-ranging discussion of suits against dissolved NPMBCs, including statutes of limitations at subsections (a)(2)(A) and (B), but review the entire section.

When considering the applicability of a statute of limitations, keep in mind that the statute for suit against the corporation may differ from the statute for a suit against an individual (the ex-director).