Mighty Mouse Secondary Button Problem

Murdered.......The VictimRight-click on my wireless Mighty Mouse started to fail last night and, by morning, it stopped working altogether, registering all right clicks as left clicks. First solution I found suggested removing the battery under the right-side. That couldn't be right… Hmm. That actually worked! Looking further, general solution was to turn the mouse off and on again. Now that makes more sense. The problem now is that Mac doesn't rediscover the mouse automatically, forcing me to set it up fresh every time right-click fails which can be as often as 2-3 hours. Annoying.
I would get another wireless mouse but MM's tiny roller ball is such a pleasure to use that I am reluctant to switch.
Update: Aha. I didn't realize that I had to push a mouse button to reconnect the mouse after turning it off and on. Rather odd design but at least I can now live with the secondary button problem (off-on-click-wait to restore right-click ever 2-3 hours in the worst case).