When you install a new battery, the RTC (real time clock) restarts from 01/01/2000. The game keeps track of played hours, so if you (for example) have played for 10 years and then the battery died you should wait others 10 years to reach the "next day" in-game.
Imho, the best solution is to adjust the RTC and set the actual time, this can be easily done with this little Homebrew software that works with DS/DS lite (the .nds version that works with DS flashcarts, like R4, that access the GBA carts through Slot-2 insertion) or directly with GBA (.gba version with GBA flashcarts, like EZ Flash Omega, and works with cartridge swap).