Don't wait for your computer to go "vintage" to do your own repairs!
Il Mio Problema
When my wife's 2011 MacBook Pro started experiencing battery problems I went to the local Apple Store Genius Bar for diagnosis. The confirmed that the battery needed replacement. Since I didn't have time that day I chose to go home and come back on a day when I was off and could get the first appointment of the day to get in and out. During the 3 weeks I waited to find an appropriate spot her model went "vintage" which means Apple no longer services it. Four days later I had my replacement battery from ifixit ready to install.
La Mia Riparazione
I have worked on a lot of older computers replacing all manner of parts so I am fairly confident at doing any work that does not involve soldering. However recent Apple products have gotten a lot of coverage for being "less repairable" than ever so I was concerned. However, this model clearly predates those problems. The battery installation was by far the easiest replacement I could imagine. It literally took less than 10 minutes and was extremely easy if you are organized and follow the guide.
Il Mio Consiglio
1) Keep your screws separated and organized by where they came out of the machine
2) to repeat Keep your screws separated and organized by where they came out of the machine this is CRITICAL
3) Get the right screw driver for the internal battery screws. The exterior screws are Philips but the internal ones are Tri Wing which is not common. I was able to successfully remove them with a very small flathead screwdriver but it was challenging and clearly did some damage to the screws. I should have gotten the right tool for the job.
4) If you have one of these computers keep it going as long as possible. This computer is very repairable. In addition to the new battery I have added an SSD and combined it and the original platter hard drive into a DIY Fusion Drive to improve performance. I would also consider maxing out the RAM and adding a bigger platter HD if my wife needs it before getting rid of this computer.