This problem happens when your save file's timestamp is later than the timestamp reported by the cartridge's real-time clock (RTC).
When you replace the battery, the RTC is "reset" to zero, but your save file's timestamp stays where it was before the battery was replaced. This is a problem because the game will only update your save file's time if it's lower than the time reported by the RTC (i.e. if the RTC is counting ahead of your save file).
When this isn't happening, your save file effectively becomes frozen in time. The game simply ignores the RTC date, because it's stuck in the past. This causes date-based events like berries to stop entirely until the RTC catches up to your save file... at which point the RTC will probably be running dry again.
Some events, like Shoal Cave and Match Call, work regardless of the above because they only rely on the RTC's 24-hour time, not the RTC's date. Berries take longer than 24 hours, so they rely on the date.
As stated here, you have three ways to fix this problem:
- Reset your save file. This will replace the timestamp on your save file, meaning the RTC will count ahead once again.
- Manually alter your save data to bring it behind the RTC time (and therefore the RTC will be ahead again).
- Change the RTC timestamp to be roughly the same as your cartridge timestamp, or ahead of it.
The latter two options require access to homebrew or save file dumping, which is difficult to come by for old consoles like GBA. If you have a DS Lite/Phat and a DS flashcart, you can load software (example) onto the flashcart that will change the RTC in the inserted Game Pak. If you can dump your save file, you can change the RTC data using PKHeX.
Apparently, there were also GBA flashcarts that would load software onto a GBA console then allow you to insert your cartridge and change its RTC timestamp. I don't know how you'd come by such things in 2022.