As others suggest, AC coils used on DC will draw a greatly excessive current and be rapidly destroyed, this could certainly happen in one minute.
If the contactor is not fully pulling in due to dirt or rust, then that would also cause excessive current and coil failure, with an AC coil.
However in my experience, the extra current is not so great as to destroy the coil quickly, it seems to be more of a long term problem.
DC coils can not be damaged by the contactor not fully pulling in, the current is limited by the DC resistance which is not influenced by the closure or otherwise of the magnetic circuit.
"universal" contactor coils that work on AC or DC are available here in the UK and presumably elswhere. They are a DC coil with a bridge rectifier built in, therefore the coil only sees DC, even if the supply is AC.
They are used when silent operation is required, and to reduce spares stockholding, since the same item can replace an AC or DC coil.