I am sorry. I was talking about "import preset".
I click "import". There is import preset "none". I select import preset "my-name". I import photos.
Next day I click "import". And there is again import preset "none". But I want to be last used import preset ("my-name") automatically.
"sort by capture time" is not stored in import preset (it is not possible) but I want it always to by "sort by capture time" by default (not "none") - how to do it?
All these settings get set to own its own when you start using any presets, may be in your case Lightroom not saving the last action on the import screen.
You may try and reset the Lightroom preferences back to default and try using the presets after that.
Usually, it keeps the values selected with the last import.
Make sure LR has full access privileges to all folders needed by it.
What is your OS?