When my PSP says it's sleep-time

This happened twice, both times as I played Crisis Core.
     The second time it happened, Zack was in this snowy area and fought a lot of monsters (and gained some gil on the side!).  Already, the green power light on my PSP was flashing, and it was for at least ten minutes.  Then, I come across this powerful enemy with one wing (not Genesis), stronger than the usual monsters.  During the battle the DMW was activated.  I thought "Oh my gosh, I don't NEED that right now, I gotta find the save point from all the way back near the beginning of the area...!"  So it was going to match three faces ( forgot which character already) but then it switched to summons mode, and by a lucky spin, it was Ifrit.
     Lucky?  Uh, NO!  That's because the cinematics showing while Ifrit prepares his attack take up...... BATTERY POWER.  Oh no, oh no, oh no, please hang on, hang on!  I want to save!  So the battle was successful of course, Zack being Zack, and me being Zack and all that.  I had Zack run run run to where I thought the save point was located (no map available there).  I was sure I was really close...
     And then the PSP turned off on me.
     For those who have a PSP, I have some advice.  Take it from me.  If this happens to you in the middle of playing a game, wait for a minute or two, and then turn the unit on again. There should be enough battery power left to do the next thing if you do it fast. Right after it is turned on, push the Home button and stop the playback of the UMD.  In other words, you have to quit the game.  I read it's not a good idea to take the UMD out if the game hasn't been quit.
     It should allow you to safely take the UMD out before turning off on you again.  I learned from this and it took me two times.  Now I always check my battery power before and after playing, and when the green light is flashing, I plan on saving or stopping as soon a possilbe...or right away if I have to.