As you might guess from Ron's reply, and many others you might find if you crawl thru the archives here, the best place to store an RCA remote is the trash can. Actually that's the best place for most cheap remotes.
IMHO, the best brands for cheap remotes are One For All and Radio Shack. The cheaper OFAs will still lose their programming when the batteries fail, but the slightly higher end ones (like the $19 URC-8811 or URC-8810w) will do everyting you want.
Rob
http://www.hifi-remote.com