My understanding is that, no, the rule may not be suspended.
That being said, there is a vast difference between suspending a rule, and superceding it. Adopting a special rule of order is the way to go here: any adopted special rule of order overrides the adopted Parliamentary authority.
However, I don't see that you've stopped to consider why unfinished business falls to the ground when an assembly with members with defined terms of membership has some or all of its member's terms expire. My opinion? It's because otherwise it would force the new, incoming members -- who haven't yet debated, researched, or otherwise considered, the pending unfinished business (and who perhaps, for that matter, haven't yet even heard of them!) -- to go up against the other members, who presumably have had plenty of time to debate, research, and consider them. In other words, without this rule, the incoming members would be on an unequal footing with the incumbents. By forcing the unfinished business to fall to the ground, the rule forces those unfinished issues to be taken up de novo -- that is, "as if new," or right from the beginning, all over again. That way, everyone gets an equal crack at them.