Step 1: Recall the concept of economic depth.
The economic depth of surface mining is the maximum depth at which mining remains profitable.
Step 2: Identify the governing factor.
This depth is controlled by the break-even stripping ratio, where the cost of removing overburden equals the economic value of the mineral.
Hence,
\[
\boxed{\text{Break-even stripping ratio}}
\]
is the correct answer.
Therefore,
\[
\boxed{(C)}
\]
is the correct answer.