I found online that you have a chance of failing to get the treasure, but if you come back in 16 days you can try again. Just to make sure I moved around for 16 days then checked all the towns again and I still have no propositions.
I don't believe it's possible to permanently miss a treasure, I've played this game many many times, but it seems that this has happened to me.
Is this a known bug? I can give you my save file too if that's helpful.
Edit:
I'm dumb and never knew there were propositions only available on certain months.