Yep, I'd agree it is the battery going. The optical out circuit is always on, so it makes no difference from a current draw perspective whether you've got equipment hooked up to the optical or just have the cap on.
I've had a couple of my old SLA batteries go bad in the space of a couple months last fall. Both were fully charged and didn't run the V3 nearly as long as they should have. Seems like when SLAs get too old, they stop holding as great a depth of charge so their amp-hour capacity goes way down. This seems to happen fairly abruptly, not slowly over several uses. One day they're fine, the next day they're not holding their usual capacity. I've since replaced my SLAs with Li-Ion batteries.