Cordless optical mice eat batteries, fast enough that some
have moved to AA instead of AAA batteries, which are roughly
2.5-3X the capacity and still you might not get 50 days out
of a pair, but with AAA I'd expect a month isn't even
possible unless you accept poor function as it runs
batteries down to nothing, below voltages normally
considered drained. You could get 2 pair of rechargeable
AAA.

With my Wireless Intellimouse Explorer 2.0, I get 5-6 months of heavy, daily
use on AA. The wireless mouse I had prior ( also a WIE ) only got about 1.5
months out of AA.

YMMV.