FWIW in an OMC I'm involved in our accountants insisted a Director who was not in good standing with the company (had some arrears) be removed at the next AGM before they were comfortable signing off on our accounts. You might also find a similar condition written into the constitution of the company, though in our case people in arrears mostly lose their ability to vote at General Meetings, there was no specific bar on them becoming Directors.
Given the issues with getting all members to pay their fees I think it's pretty important that Directors lead from the front. I personally wouldn't support a Director in arrears for this reason, there's too much scope for other members to say "Well if it's OK for him/her to have arrears then it's OK for me".