Started having problems with DS1307. Thought it was the battery, but after two replacements realized that either the program was re-writing registers or the chip was bad.
Replaced the chip two weeks ago. Reprogrammed the 16X2 LCD display to show times from the DS1307 [lower] and PCF 85263 DemoBoard [upper].
Picture was 4/21/2019 with a difference of 31 seconds. Checked today, now 30 seconds. Initial difference was about 36 seconds.