Don’t let your air pressure (breath support) drop between notes! Keep the pressure on, just like when talking. This way, you connect the notes together nicely, and they become a real sentence. Of course, you stop blowing when you put a comma or for breathing.
If you have to play short notes in a row, it is wiser and more relaxed if you leave the pressure on but close the airflow with your tongue. And especially, do not breathe in between all those short notes; you get tired of that. It is less tiring to play with constant breath support, and it sounds more natural.
Tip:
Try it out with a piece you can already play by heart, or else with some song that you can already play well while reading. Just compare how it sounds when you play-in-sil-la-bles (see item 06) or more portato (with constant breath support and not too strong attack).