It is not possible to give an exact answer to this question for the following reasons:
known deposits are being worked and new methods of copper extraction are being developed e.g. using bacteria to 'eat' the copper out of low grade ore
some deposits do not contain enough copper to make them economic to extract
there are many copper deposits that have not yet been found
deposits are still being built up on the seabed.
Picture 8. The copper strip stays shiny because it is relatively unreactive - this makes it ideal for recycling.
However, copper can be regarded as one of the few metals that is fully sustainable. By this we mean that we should never really run out of copper. Copper and its alloys are totally recyclable.
As a trace element in nature, it also cycles through the entire food chain. Copper that washes out of rocks and soils will eventually reform as deposits on the seabed.
It is important that we do try to use the copper that we have sensibly and recycle as much as possible. Whilst we shouldn't run out, the demand for copper is growing and this may lead to shortages in the future until new deposits can be mined economically.