I2C with DS1307 hang after end of transmission
[Reposting my comment as an answer]

What sense would it make to hang the write if the slave doesn't ACK? It's not like it might come back later; it's missed its chance. More likely, the DS1307 is holding down the SCL line. The master would interpret this as a "clock-stretch" and could wait indefinitely for it to be released. As you say, you may have damaged the chip or you have a short on the package.