To dynamically hedge a long call position, we need to hold dC/dS amount of shares. That number is equal to the delta of the call. In practice, given an option position, people adjust its delta hedge on a daily basis, but in theory, rebalancing is a continual, non-stop process.
The call delta BS-formula makes it clear that “t” alone will change the delta even if everything else held constant. Specifically, even if S is not changing and interest rate is zero, the option delta won’t stay constant as maturity approaches, so we need to adjust the number of shares we hold.