If you think about this for a moment, you will realise that if it were to slow down the RTC device every time you were reading its registers, you would be just as well performing the RTC function inside a loop in your Micro. The whole point of using an RTC chip is that your reading of the values does not interfere with the RTC device keeping time.
Read the device as often as you like. Oh and read the datasheet for the DS1307 again while you are at it
If you have a timekeeping error, check that your crystal is running at 32.768Khz and the frequency is not being pulled by poor board layout or a bad connection. Breadboard for example, is notorious for this because the wires from the crystal are so thin that they barely make contact.
I built a heating controller for home with a DS1307 and it has been running now for 9 years. The code reads the DS1307 several times a second and it has never 'lost' time. In fact it gains about 5 minutes over 6 months. (I only reset it when I'm changing from BST to GMT or back) The circuit is built on solder pad-board so the crystal connections don't exactly conform to best practice