I don't know if your chapter is anything like mine in this respect but we have a Constitution AND By Laws (2 seperate documents).
The primary difference is that bylaws can be suspended by a 2/3 vote of the members. If this were the situation at the Mu Tau chapter of Sigma Nu as long as the guy's GPA isn't below what the University requires of officers then we'd just vote to suspend the bylaws and keep him in office.
Otherwise my advice (since you asked for it

) is do exactly what Tom said. If you start only obeying the rules that you LIKE in your constitution you've missed the entire point of having one. You may as well burn it because unless your executive council follows it, it's worthless.
That doesn't mean that you can't change it though according to the rules that it probably has laid out.
LHT
Kevin