For anyone else having these issues, definitely call or email Apple.
I second this, and not just for the remote issue. If they get enough calls on a problem, maybe they will look into it.
For the people that really don't want to call, I know that calling support lines usually sucks, but calling Apple support isn't too much of a hassle.
I have used Apple products for over 20 years, and for some reason, I have had to call Apple support more times in the past 2-3 years than the previous 20 years combined. Surprisingly, the wait times have been relatively short, unless I was put on hold. The support representative are hit or miss. Some are knowledgeable, and some are not.
I was having issues with iTunes Match a while back, and the support rep I ended up getting clearly had no idea what iTunes Match was or how it worked. Frustrated with her incompetence, I politely asked her to transfer me to someone else, and she took offense and started getting rude. I think I ended up hanging up on her.
But, I have also had some very knowledgeable reps that were very helpful.
If anything, you can create a record showing that you are experiencing this issue. So, if something happens with the remote batter after the warranty period, you have a record of issues with it, and maybe you can get it replaced.