I've had this remote for just under a year and recently it's not been holding a charge very long, a full charge only lasts a couple of days. Can I buy a replacement battery?

Yes, you can.
[Link: buylogitech.com]
Are you sure you needed one? My charger was not making contact with my remote very well and it was not charging well, and my battery wasn't lasting more than a day. Every day of use, it would be almost dead. So I put solder on the tabs on the remote base and it is not making better contact and now after a full day it's still at 3 bars of battery.

I'm pretty sure it's charging, it's going from one bar to three every time I put it in the cradle.

Mine did too. But it seemed like it would not hold a charge. What would happen is that it would "couple" and then "decouple" to the cradle. It would do this over and over and over through out the night and I never caught it. I think that confused the "gas gauge" and it told me it was full when it wasn't. It looked like mine was charging fully too. It would be at 3 bars in the morning and then when I used it through out the day it would go down to 1 bar.

I have done enough work with these batteries and gas gauge chips to know it's easy to get them confused. I don't know exactly how this was showing me 3 bars with the amount of charge I put into it, but it was. Maybe it's a software bug.

Due to the known problems with the chargers for these remotes, I decided to look into mine. And I had it docked in the cradle for a day and watched it (when I was around) and I noticed that the screen showed it was as if it was being set in the cradle and then removed over and over again. Sometimes it took 30 minutes to an hour for a cycle. Sometimes it took 3 minutes.

When I took it off the charger it said 3 bars full, but it lasted about a day, it would have not lasted 2 days.

I took the base apart, put solder on the contacts and put it back together. Now when I put it in the cradle, it makes contact and never "decouples". Now after a night of charge and a full day of use it still has 3 bars on the screen. I never changed the battery.

Buy a battery if you want. But I'm just giving my experience. I thought my battery was not holding a charge, turns out it was the charging cradle and a glitch in the gas gauge for me. So I saved the $30 I was going to spend on the battery. I was about to buy a battery or throw my 880 in the trash and buy a One, it was when the One was just about to come out and I was counting the days cause I didn't think my battery/remote was going to last. I did that fix and now it's 100% better and lasts days on a charge and I have not had the urge to replace the battery or remote.

But do what you want. Your problem might not be the same as mine. If your charging cradle is 100%, then it might not be the problem. Mine was finicky.

Sounds like that's worth a try, so you took the cradle apart and applied the solder to the back of the contacts?

Try an easy solution. The charger sucks you can try the quick fixes but they are only quick not so reliable fixes. I got a new charger that I found on ebay when I did a search for "logitech charger" This worked for me with my 880