The method 'switching to Flash 128k Memory' is what people usually recommend. Unfortunately, this method can only be used for Emerald. I used it before, it worked! But for Fire Red, the answer is NO! The only solution for this damn situation is downloading a new ROM from a reliable website.
I'll give you the link: http://www.coolrom.com/roms/gba/14488/Pokemon_-_Fire_Red.php
This should cure the goddamn 'save error' disease. However, here is the bad news: you'll have to start all over again so I sincerely hope that you didn't figure the problem out too late.
P/S: I got this same problem yesterday, and I've just found the solution for me and... for you as well today. Lucky, huh?
P/S 2: Damn, you still play Fire Red? And I thought I was the last one who did that.