How deep can I dig in the diamond mine?

Solution 1:

The following gameplay video shows that the game goes on till you fail. After 980 meters, the gauge displays "MAX" instead of meters, and you can dig till you fail.

Solution 2:

I don't know if there's a limit: presumably, you win at 1,000 meters, given that the depth meter has only three digits.

Here's, however, a youtube video showing off a depth of 960 meters. Keep on digging!