Maybe it's just the battery draining... it's definitely worth trying to replace it with a new one - it looks like a CR1225, right next to the compact flash marked "POSITION 1" in this photo:
https://supportforums.cisco.com/sites/default/files/legacy/9/5/3/86359-RSP-720-3C-GE%20512%20MB%20Flash%20identification.JPG
[edit] According to a reply here, there are two batteries on the RSP720 that should be replaced:
https://supportforums.cisco.com/discussion/11090226/cisco-7600-rsp-reload-continuously