Loosepuck

Long time lurker, first time poster. I am having battery issues and not seeing my exact sitch, so I thought I would ask about it.

I drive less than 3 miles to work and have seen my mileage drop from 45 to 38 mpg. Then I recently got the red triangle/full dash flash of death. My battery had dropped to 9 volts with these short runs to work and colder temps. I have been trickle charging at 2amps for a few days and took a 2 hour drive yesterday. My battery still measures only as high as 11.8v after rest.

I am hoping I can boost this battery back to life, but from what it seems here, it is toast. It is a yellow top with unk date, obviously the second battery.

Should I keep trying to trickle this one back to life, or just buy another? The new yellow top is $289 at my local o’reilly. Ouch. Am I just burning fuel to try and top this battery off when running in to work?
Thanks in advance.