That sounds odd and quite different to my experience with the game, but I have it on Steam, not the GOG installer.

However, when I do quit the game I use the Save & Quit option. Every time it remembered which checkpoint I was at, so was never a problem.

EDIT: There is the possibility that I'm confusing this with Trine 2, which definitely does have a Save & Quit option and remembers the checkpoint you got to.

---redacted---

I bought this game on GOG.com and there is no Save & Quit option. I also downloaded Trine Demo from Steam and again there's no such option available - the game only allows to use Quit. And after you choose Continue from the main menu it takes you to a level's beginning. However, while in the game you can choose Return to Last Checkpoint and it will take you to, well, the last checkpoint. But as soon as you quit and then choose Continue the game starts from the last level's beginning. I haven't progressed far through the game so I can't say anything about "Town Portals" or whether the game is going lo save checkpoints after that but right now it doesn't. And there is no manual save - the manual clearly says so:

"Trine saves progress automatically between levels. Once you have completed a level, the
game is saved and you will be able to play that level again in the Choose level menu. There
is no manual save in the game".

Edit: I've found a post from a developer of Frozenbyte who explains this. In short, Trine engine doesn't support mid-level saving. In Trine 2, however, they fixed this. The developer also suggests a few cheats to warp through a level but I can't say it's a compelling idea so personally I won't use it. http://www.adventuregamers.com/forums/viewreply/12116/

I am terribly sorry. I honestly thought this thread was in the Torchlight section, not the Trine section. My mistake.

Yes, checkpoints only work for dying and retrying. If you quit the game, you have to start at the beginning of a level.