I2C RTC returning bad times - sometimes
Such intermittent issue looks to me a hardware signal integrity problem, specifically around the I2C bus RTC chip. Did you experience any problem from any other device on the same I2C bus (e.g. when all the LEDs are on)? If not, then check on the noise level on RTC chip power and GND. Also, the I2C spec has limit on the bus capacitance load as max as 400 pF. When there are too many I2C device loads on the same bus, the bus may become vulnerable to the system noise. 

Debug Suggestion: To narrow down if it is I2C load issue, add an I2C bus driver chip between the main Arduino board and your peripheral. For example, P82B96 from TI. See the spec here. http://www.ti.com/lit/ds/symlink/p82b96.pdf