I have seen similar situations where one or more PC's would rather fight an impossible battle rather than surrender or lose equipment. One player actually tore up his character sheet at the table because his character lost a level to an undead attack. These situations happen for a number of reasons but the number one reason for this attitude is that the player has no real investment in the character. If the character dies, so what? Roll up another one and keep going.
The reasons for having no investment or care for the character can be the fault of the player, the DM, and/or the game system. The player needs incentive to keep the character alive at all costs even if it means suffering temporary setbacks. One way to encourage this care is to reward successful play with more than just impersonal "stuff" such as magic items, XP, and gold. If a character develops meaningful social connections and gains influence with persons in power then they will have earned rewards that a new character cannot begin with.
In order for these rewards to be meaningful they have to be of some actual benefit to the character that the player perceives as valuable. If a player is faced with a no-win situation where it comes down to giving up gear to stay alive, he or she may be more willing to consider it if there are known NPC allies that will provide gear, with no questions asked because the PC saved thier life on a past adventure. In this case, the replacement gear along with an opportunity for sweet revenge would be much better than just committing suicide and starting over, especially if the character had many other personal,non-transferrable social assets.
The DM and the players have to work together in order for these social assets to function. The DM has to ensure that they have actual value and the players need to recognize that value.