The 2nd ed 'Manual of the Planes Web Enhancement' includes:
Individual promotions occur seemingly by accident. Since modrons have no individuality, there’s no point in trying to promote the 'best and the brightest' — all modrons of a given rank are equal. Thus, the nearest one of an appropriate rank is promoted when a vacancy occurs."
I am interested in what happens to the monodrone gap that is eventually created by the chain of promotions.
'Manual of the Planes Web Enhancement' :
Monodrones, having no castes below them, reproduce by fission to replace lost members.
So it looks like when a monodrone is killed or promoted, a nearby monodrone splits into two monodrones but that is contradicted by the Planescape book "The Great Modron March" :
When a modron dies, it disappears. Some have described the process as rapid decomposition or corrosion, but in the end the modron corpse simply vanishes within seconds. Its essence reverts to Mechanus instantly, where it forms into a new monodrone. If a modron of a higher rank than a monodrone dies, a modron from the rank immediately below is 'promoted'. Then one from the rank below that fills in the void created by the promoted modron, and so on.
Despite some reports, modrons do not reproduce by 'splitting'.
The TGMM explanation makes practical sense as otherwise the army would just keep regenerating - any remaining monodrones could keep splitting into replacement monodrones.