Simple answer? It's magic.
OK, but seriously...
The natural world, and all non-magical objects within it, exist at an uncharged base state. Magic taps an energy source and performs some alteration on the target, but at the same time it produces a strong magical charge in that target. Since like charges repel any attempt to perform further magic on an object that is already magically charged will fail.
Depending on your story requirements you could have this charge dissipate over time as the object's new state becomes the new normal, allowing a transformed statue to be transformed again once the charge has grounded out.
The biggest flaw I can see here though - and forgive me if this is a frame challenge - is that a 'charged' object becomes effectively immune to magic. I'm going to go out and get some mage to enchant me with, I don't know, a cleaning aura. Boom, I'm immune to magical attacks. Physically conjured objects will still work on me, but direct magical interactions are a no. Similarly I can get my gear minimally enchanted and be immune to direct magic without having to worry about getting myself permanently cut off from magic.
Instead of letting trivial magics ruin the fun for everyone perhaps a spell's power level is the determinant for what future magics can affect something. If I get a trivial enchantment to get rid of acne that's not going to have enough of a charge to ward off an elemental attack. An act of pure creation on the other hand results in an object that is almost completely composed of magical charge, so anything less than the ultimate power level will be ineffective against it. So your plushie is safe, I'm probably safe from magically-induced acne... but a strong enough spell could still affect me.
Of course this charge might only count for certain types of magic - transmutation, conjuration, enchantment, etc. Elemental magics probably act on the element, not the target. A fireball spell produces actual fire which acts like fire normally does, so a conjured or altered target is still going to burn. Other schools of magic might produce effects that are transitory and leave no lasting charge. Evocation, abjuration, illusion, divination... lots of possibilities for magic that still works.