OK, so are you saying anything I said was wrong?
Well yes, though it was really a minor misunderstanding of the technology. You said...
It is only the long range functions that will stop, such as getting pictures from rides automatically on your account.
... when getting ride photos (as well as ride personalization and BOG location and probably a few others) is actually one of the tasks handled by the unpowered medium range 915 MHz second radio. Not a huge thing either way if the operation of the long range powered radio chip has no effect on the function of the two unpowered RFID chips in the Magicband.
As you say...
From everything I have read, the magic bands will work forever for park entry and fast passes.
But that may not be a safe assumption. Disney invested a Billion dollars into developing the Magicband system. The majority of which went towards the powered (long-range) 2.4 GHz radio transmitters portion of the Magicband and the extensive network of 2.4GHz receivers and the server and storage devices and software on the back-end needed to process and keep that data and make it available in a useful way.
Think of it this way, the first radio in your Magicband handles Park entry, FP at the attractions, Touch to Pay, SotMK Key, and resort room entry. All the stuff that makes a guest WANT to wear the bracelet. The second radio provides more guest services. These features are what Disney gives us in exchange for us carrying around the third radio. The long range chip doesn't really do anything that will affect the individual guest experience in any direct way.
In the practical sense of the word, I do not believe that a Magicband will continue to function if it's battery is dead.
I mean, the first two radios are passive and they will do their thing every time they get energized by a tapstile or from a portal reader (what they call the reader for this type of rfid system, like the highway toll account systems). There's no reason they couldn't continue to work, but Disney didn't invest all that money just to let you get all the goodies and them lose out on your tracking data. The network back-end knows that if the RFID scanners are picking up your Magicband then the 2.4GHz receivers should be picking it up as well. If it's not then it must be because the battery is dead or the Magicband has been damaged.
If your long-range chip stops working, the network will flag your Magicband and in short order you'll get errors when using it. The CMs will direct you to GR or the resort front desk and they'll swap it out for a new one. If it's failing because it's very old they might ask you to purchase its replacement but I doubt that happens too often. In that case there is still the option of being given one of the RFID cards which I believe only feature the first, near field, RFID chip.