In my opinion, the least of the issues with reflex sights is the battery v. no battery argument. A good red dot sight such as an Aimpoint will be more reliable than a reflex sight. Here's why:
While there is a chance of an Aimpoint failing it is infinitesimally small. They are built that well. Battery life is about 4 years with a T-1 and over 5 with an M-4 if left constantly on at setting 7 out of 12. The batteries are small and light. the hermetically sealed AA module for the Magpul MOA pistol grip will hold 4 CR2032 batteries in their sealed blister packs. That's 20 years of battery backup on tap for a T-1.
Since it relies on ambient light for illumination, A reflex sight will have the reticle disappear or "washout" if you are in a dark enough area looking into a light enough area. As it is best not to fight fair in war I can imagine many situations where you might be in a dark place shooting at targets exposed in the light. Or in a home defense/ PD situation you are in the dark and shine a powerful weapon light on an intruder/suspect the reticle will be washout and be hard or impossible to see.
This leads to many more practical situations where the reflex sight will, for practical purposes, "fail" as in fail to produce a usable reticle image when having one is conducive to survival.
On a red dot you can crank up the power to meet the need of your environment, on a reflex you don't have that option. Also, when you increase the brightness on the red dot, it makes the dot look larger as well. So for precision you turn your 2 moa dot down to just visible and crisp. For fast and close crank it way up and it looks like a 4 moa big n bright.
Additional considerations are:
Reflex sights tend to be bulkier and heavier than RD sights.
Reflex sights, like the Trijicon RX-30, can have complex suspension/mounting systems that can hide more gremlins than a comparable red dot mount.
Open reflex sights like the C-More and the Trijicon have an emitter hole about 2mm in diameter on the top rear deck area where the light shines out to project the reticle on the lens. If any debris gets in there the sight will not function until that small orifice is cleared. If any mud or debris gets on a red dot it's usually fairly easy to wipe or rinse it off.
For me I chose a Trijicon TA-33 ACOG (even if no fiber optic illumination the black reticle is still there) for my recee build and an Aimpoint T-1 with fixed irons for my KISS CQB to 300 m. build.