Most of you have made great comments, so I don't really have anything to add to the suggestion itself. Instead, I have a suggestion for those of you who get sucked into the boss battle of an event without meaning to... If your combat is no longer in a valid, accessible, area, you will be taken out of battle. In other words, if you get sucked into an event's boss battle but don't want to fight it or can't win, just wait a couple of minutes without fighting for someone else to beat the boss and the event to end. Go play Jinxie's Jamboree or browse the forums if you're impatient. Once the event is over, you're no longer in battle and can go about exploring as per usual without any penalties.

I believe said trick won't work in the case of an event in Fungus Grove or Faerina's Shrine because the areas are an actual zone, unlike the town ones where the system resets it back to being a town after the event is over.

Yes, this is a really good idea, especially in the cases of boss fights. a good 10+ times i've gotten into them and had already used a healer, (while also being low on gold and having no revives) and having to fight merely to lose and wait half an hour just to revive these pets. losing some gold would be fine, or maybe the mana can get wiped clean due to trying harder to escape, or even the mend counter could be set to the 25 turns before use or something(which might be a bit smart, considering if you escaped a battle you could just heal your pets before moving on, and therefore shouldn't need it quite so immediately, making it more of a minor annoyance).

the idea of limiting the opportunity to run away idea isn't too bad in non-boss battles, kind of like waiting a turn for potions, but for boss battles it's probably a little unnecessary.

would it apply to storyline bosses though? like if you went into the battle with them and realized you're not quite ready, and you'd rather go and prepare a bit more before taking them on? honestly i'm half and half on that one, since they do come quite suddenly, but at the same time it IS a storyline boss battle, and in most games if you don't do it the first time, you have to try again and again till you get it. just figured i'd mention it, at least.

Storyline boss fights also generally give you a warning, and you can stop during the bosses little spiel and go do whatever else you'd like. There are a few bosses that as soon as I saw that I ran off to go heal, reequip, and all my other battle prep.