All wireless mice do this.. Well opticals anyway.
They go into a low power mode where the LED flashes only once or twice per second. The flashing is just to detect movement. If it didn't flash the LED it would never know it was moved and never wake up!
2 weeks seems fairly normal for AA batteries. Especially if you use the mouse at least 2-3 (or more) hours per day. But it varies my mouse model. Some use power more conseratively than others. It can also depend on your mousing habits.... For example I have a tendency to move the cursor along the line of text I am reading, thus I'm keeping my mouse active all the time.

(I have a Logitech MX700, get about 5-7 days worth before it has to hit the charger...) If I didn't do this it would most likely last longer.