Hi all,
Should anyone face the same problem, I found the root cause: brownout threshold. I burned a new bootloader (Optiboot 8.0) without such trigger and the node has been working with used batteries (~2.7V) since May.
Hope this helps.
Don't ask me why, but now it works. I changed nothing! Went to my girl over the weekend, coming back, the node was registred. Maybe a jammer went away?