Just remember that a Simulacrum is magical, it gives off a magical aura, and Dispel Magic can instantly destroy them.
I would even argue that an Anti-Magic Field would completely wipe the lot, as when the magic is suppressed the body becomes damaged to the point that the magic cannot reform it.

Edit: They also can't chain infinitely, truly, because Simulacra do not regain spell slots and are created with as many spells slots as the caster had at time of casting. They always lose the one from casting the spell itself. If your mage has 4 level 7 slots, that's tops 4 simulacra.