Most skimmers will remove plankton and trace elements as well as protein waste from fish food and waste. If you have the skimmer on 24/7 there is a chance you will need to add supplements and you probably won't have much plankton in the tank, (regular water changes will add the missing trace elements and you won't have to worry about the supplements).
Most people run skimmers all the time and just don't keep corals that need plankton, or add liquid plankton foods a couple of times a week.
Other people run their skimmers for a few hours immediately after they have fed the fish. The skimmer removes most of the protein waste and then it is turned off so minimal plankton is removed.
The choice is yours. If you have corals like Gonioporas and Tubastrea, you should reduce the use of the skimmer. If you have a tank full of Acroporas then you can have it running all the time, but do regular water changes to keep the trace elements up (or add supplements).
Skimmers also remove chemicals (turpenes) that are released from soft corals. If these chemicals build up they can cause problems to the others corals in the tank. Most soft corals will release this during the first 6-12months they are in a tank. Then they settle down and stop doing it. However, if a new coral is introduced after that time, they will start again. It is their way of fighting and telling the new coral to go away. Carbon will absorb turpenes.
The easiest way to tell if your skimmer needs to be on all the time is to see how much foam & gunk collects in the collection cup when the fish have not been fed for a few hours. If the skimmer produces lots of black liquid during the day when the fish haven't been fed, then leave it running all the time.
If the skimmer doesn't produce any gunk during the day when the fish haven't been fed, turn it off during the day and have it on for a few hours during & after feeding.
