Question: My pro tools version is HD 10.3.7.
When I arm and start recording, everything is working, the meters going up, wave form is bulit.

And when I stop it, the wave form (aka. region) immediately disappears. This happens only to short recordings. (As far as my test goes, it happens to recordings under 4 seconds).

However, the disappeared recording is saved in audio files. It's not just there anymore on pro tools edit view.

????

Answer: 
Try this:

click off pre-roll on transport window (CMND + 1)
PT has a pre-record period whereby it will display the waveform but not record until this period is over. Logic Pro also has this function and you can disable it in preferences.