TP4056 connected all time
Yes, TP4056 is designed to be connected and powered all the time, it will automatically stop and restart charging cycles as necessary. This is all written on the first page of the datasheet:


  The
  TP4056 automatically terminates the charge cycle when the charge current drops to 1/10th the
  programmed value after the final float voltage is reached.
  TP4056 Other features include current monitor, under voltage lockout, automatic recharge and
  two status pin to indicate charge termination and the presence of an input voltage.