The temperature rating is 85C for the industrial version but 70C for the commercial.
If you are only at 55C at the DS1307 you are probably OK.
What is happening with your power supply?
Is there a derating on the battery at 55C?
How is your crystal connected? Did you use a guard plane or ring as called
out in the datasheet? Did you use a crystal with a maximum ESR of 45KOhms
and a CL of 12.5pF? There are a lot of watch crystals that will not work
with the DS1307. Also the DS1307 and DS1337 have different crystal
(* jcl *)http://www.wiblocks.com