[I think if you put a better crystal on the board](http://I think if you put a better crystal on the board)
Agreed.
The RTC 32.768khz crystals are not all equal. To add insult to injury, the load capacitance can be very different, too. Refer to the IC spec sheet and try and match the specs to the crystal you purchase. With a little luck and patience, you should be able to get within a second or so per day. On my last build, I went through 3 crystals and got to within a second every 12 hours (fast) so the software drops 2 seconds every day at midnight.
You can also try "pulling" the crystal off frequency if fast with a small variable cap of a few pF to ground on one xtal pin.
Ham radio folks may remember using two twisted wires to adjust HF gear - called a gimmick.
Ray