When I proposed the "automatic" procedure to fill vacant seats, I was mostly considering how some countries actually deal with the issue, and the best example that comes to mind is the US, where the President, when resigning or stepping down for some reason (sadly, being murdered is a rather frequent one!), is simply replaced by the Vice-President, until the next term elections come up. Other countries go for by-elections instead.
RL parliaments are handled differently thing, because iRL they have dozens or even hundreds of members, so vacant seats can just remain vacant, without a substantial difference. But of course if, say, a third of the representatives would resign, in the countries where such power is invested in the Executive or a similar branch, I'm pretty sure that parliament would be dissolved and new elections called for. This is what happens in our case, since we have such a small RA: one member resigning means 20% of voting ability being removed from the RA, so it justifies by-elections.
The problem is that representatives resigning/getting removed from office/dying is a relatively rare situation iRL, so by-elections, as an extraordinary procedure, is a valid mechanism. In our case, however, resignation is a frequent event, even in short time spans of just 6 months. That's why I would prefer a more "automatic" procedure — because we might be completely prevented from actually doing some 'governing' otherwise!
For instance, this term was a huge deception. After half the term had elapsed, we had to deal with a by-election, and, once that was over — with the RA and Executive basically stopping their activities, the RA now has to deal with an absent LRA (Shep is moving iRL), and is further prevented from meeting. The term will surely end before we have actually done anything worthwhile. I'm not blaming people in particular (or I would have first to blame myself!), but I'm concerned that replacing members of government with a super-complicated procedure will delay everything so much as to turn the democratic process impractical! And that scares me!
I had also missed Bromo's point that the RA cannot work if there is no Chancellor, because the Chancellor has veto powers over legislation, and a lack of a Chancellor means that the RA has to wait for a Chancellor to be put into office again. Geez. This is tough!
I'd be fine with most of Bromo's suggestion but get rid of the 'cooling off' period, I'm also assuming that members of Government 'cool off' before they submit their resignation, not after.