Are you using the headphone jack on the remote? If so, leaving the headphones plugged in when not in use leaves the audio amp powered on and can drain the batteries exactly as you mention.
I never use headphones. The remote was working fine until a few weeks ago when it started going through batteries every other day. I have two other Rokus w/ remotes that do not exhibit this problem.
Then yes, it likely is defective. I believe it is covered by a one year warranty, so you should contact Roku support for assistance. Note that this forum is not run by Roku support.
This page should get you started. I believe you have to answer some self-help questions before it provides you a contact phone number. https://support.roku.com/contactus It will not be a toll-free number.
Do not do a web search for Roku Support! There are many, many scam sites that offer to help, and they will have a toll-free number, but they will ask for money, or want to connect to your computer. Roku does not charge for support, and they will NEVER ask to connect to your computer. There's nothing that anyone can do on a computer to troubleshoot a Roku.