I wonder which model you have?
There are issues with pre- pro 11, I believe you can't use the lithium batteries and they have a reputation for 'eating batteries' though I would have thought you'd have to use it a great deal to use up the battery that much.
I have a Pro 11 and use lithium batteries and they last a long time, but if I'm doing long, timed exposures (which I sometimes do for a minute or longer) then the battery can get used up quite quickly.
With the Pro 11 the led lights only come on when you depress the shutter.
edit: seems to be some disagreement over battery types - I've been told by camera stores that lithium batteries are fine for the pro 11 but after web searching to check, see that silver oxide (or alkaline) batteries are universally recommended.
Don't know the answer to this, not an expert on batteries! Maybe someone else is.