Martin,
It's not filesystem related. I removed my link and started Pine fresh, in order to get some bad save screenshots for you. And managed to get it to work. The xfs thing was a red-herring.
The problem is, every time you start a "New Game," any saves to a new slot are invalid, until you save into an existing slot. Once that happens, all new saves for that session seem to be valid.
There's no game interaction in any of these. I loaded the game and went straight to options.
Brand new Twirlbround config directory, New game, nearly immediate save (unusable):
.rw-r--r-- 30k craig 23 Oct 18:56 Profile_1_A.pine
.rw-r--r-- 30k craig 23 Oct 18:56 Profile_1_1.pine
Another save, new slot, no game interaction (unusable):
.rw-r--r-- 30k craig 23 Oct 18:56 Profile_1_A.pine
.rw-r--r-- 30k craig 23 Oct 18:56 Profile_1_1.pine
.rw-r--r-- 30k craig 23 Oct 18:58 Profile_1_2.pine
Again (unusable):
.rw-r--r-- 30k craig 23 Oct 18:56 Profile_1_A.pine
.rw-r--r-- 30k craig 23 Oct 18:56 Profile_1_1.pine
.rw-r--r-- 30k craig 23 Oct 18:58 Profile_1_2.pine
.rw-r--r-- 30k craig 23 Oct 18:59 Profile_1_3.pine
4th save, in the 2nd slot (2nd and 4th slot OK, 1st and 3rd unusable):
.rw-r--r-- 30k craig 23 Oct 18:56 Profile_1_A.pine
.rw-r--r-- 30k craig 23 Oct 18:56 Profile_1_1.pine
.rw-r--r-- 30k craig 23 Oct 18:58 Profile_1_2.pine
.rw-r--r-- 30k craig 23 Oct 18:59 Profile_1_3.pine
.rw-r--r-- 30k craig 23 Oct 19:00 profile_1_2.pine
5th save, in new slot (2nd and 5th slot OK, rest unusable):
.rw-r--r-- 30k craig 23 Oct 18:56 Profile_1_A.pine
.rw-r--r-- 30k craig 23 Oct 18:56 Profile_1_1.pine
.rw-r--r-- 30k craig 23 Oct 18:58 Profile_1_2.pine
.rw-r--r-- 30k craig 23 Oct 18:59 Profile_1_3.pine
.rw-r--r-- 30k craig 23 Oct 19:00 profile_1_2.pine
.rw-r--r-- 30k craig 23 Oct 19:01 Profile_1_4.pine
Go back to main menu and start New Game, save (fail), then save again in the first slot - two slots OK:
.rw-r--r-- 30k craig 23 Oct 18:56 Profile_1_A.pine
.rw-r--r-- 30k craig 23 Oct 18:56 Profile_1_1.pine
.rw-r--r-- 30k craig 23 Oct 18:58 Profile_1_2.pine
.rw-r--r-- 30k craig 23 Oct 18:59 Profile_1_3.pine
.rw-r--r-- 30k craig 23 Oct 19:00 profile_1_2.pine
.rw-r--r-- 30k craig 23 Oct 19:01 Profile_1_4.pine
.rw-r--r-- 31k craig 23 Oct 19:06 Profile_2_A.pine
.rw-r--r-- 31k craig 23 Oct 19:06 Profile_2_1.pine
.rw-r--r-- 31k craig 23 Oct 19:07 profile_2_1.pine
All of these files, for a session are identical. The only difference is the names. It seems like you need a lowercase profile_*.pine for saves to be read by the game.
As a final experiment, I deleted the Twirlbound directory, again, started a new game, played a bit, saved (failed), then exited, renamed the Profile_1_1.pine to profile_1_1.pine, and started pine again. The save session is there and valid.
The bug looks like some kind of lowercase/uppercase issue with your save file naming.