I bought a ship and went to go sell stuff I farmed and when I came back the ship I bought was gone! How do you keep ships after you purchase them?
Before the NEXT update, you would've needed to own a Freighter to own multiple Starships. All of your ships would've then been transported to your Freighter, should you leave it somewhere.
Now, owning a Freighter is no longer necessary to possess multiple Starships. Without a Freighter, you'll need to summon your Starship instead.
Simply open the quick menu (D-Pad down on gamepad, x on keyboard), navigate towards "Summon Vehicle", then take the right-most option to see a list of all Starships you own. Simply summon the ship you want, and it'll land right where you wanted it to.