These remotes don't use that much power, and should not be draining FOUR batteries that super fast. Normally; I would immediately suggest calling Bell and explaining your remote situation, IF this were a new remote. Try anyway, see what they suggest or do.
You shouldn't ever have to change batteries for remotes like Bell's, or most remotes for electronics as you've been doing so, ever. There are those other remotes, like from Logitech, etc. that you sit in a cradle to charge up though.
I've seen customers with original legacy remotes that work perfectly, and then I've seen customers with badly and mistreated remotes from fairly new systems. So as far as wear'n tear, maybe you're just sleeping on it...and draining the batteries. Who know's, equipment can just plain fail sometimes too.
Get a new one! GL