On PSO PC, your character saves files are your responsibility! They are not saved to the server, instead, your character save files are saved to the Backup folder of your PSO PC installation location. By default, this is:
C:\Program Files (x86)\SEGA\PhantasyStarOnline
Depending on your Windows permissions, they may also be saved in (by default):
C:\Users\NAME\AppData\Local\VirtualStore\Program Files (x86)\SEGA\PhantasyStarOnline
Make sure to back up your save files often.
Please also note that your save files are tied to your Serial Number. Changing your Serial Number will not allow you to load your save data as the game will report it as corrupted. Therefore, it is important for you to keep a record of your Serial Number/Access Key in the event that you need to restore your save files, as they can only be loaded when using the same serial number.
You can check your serial number and access key in the options menu of the launcher.