Ah, ok. If those are enough light, then you're good to go.
You didn't use any current limiting resistors in series w/ the LEDs, which is why they started to die. If you use a constant voltage source, you will need these resistors. Otherwise overcurrent will kill them.
The tricky part: the LED is an active load, it has a dynamic 'resistance' which makes it tricky to select a resistance value for said resistors to run them at the correct current. In the case of these 5mm guys, the manufacturer states 30mA MAX, at 25c ambient (room temp.) All of their specs and testing were done at 20mA. This is common. You would want to run these LEDs at 20mA, constant current. See first attachment from an earlier LED discussion, this will get you a 20mA const. current for each LED, which is technically the way to go. You'd need 33, instead of the 5 shown, and they'd all be white LEDs, but you get the idea.
Now the only problem, voltage overhead. You said the battery drops to ~11V at times? This will be an issue, if the Vf of the LEDs are higher than about 3.25V. The LM317 as shown drops 1.25V across the resistors, so w/ 11V in, you're getting 9.75 max out. If the Vf of your LEDs are 3.4V typically, you're going to be running them at less than 20mA when the battery dips. A possible way around this is to use discretes; two transistors and a couple resistors for each leg of 3 LEDs to supply a constant current, this would lower your overhead to the millivolts, but may add cost, and a little complexity. That's probably the way I'd go, though.
If you try to regulate the voltage (instead of the current) with the LM317 as you had first suggested, then you're still facing the same issue... 1.25V dropout. But, let's say this IS the way you want to go, you can try to regulate the 12V to 10.5Vdc, using an LM317 (rated for 1.5A or higher, btw, and heat sink it) as you suggested earlier. Then you will need to add a resistor in series with each LED leg. Using the typical Vf from their datasheet, you'd be looking at ~10.2Vdc for each leg (3.4V each LED.) You need to drop the extra 0.3Vdc across a resistor:
(10.5 - 10.2) / 0.020 = 15 Ohms
See second attachment. Edit: And I don't condone running it this way, Vf is the issue. Each LED will be different, some LEDs will be running less then 20mA, some more, etc. etc. Making any sense? Sorry it's a little long winded and cluttered. hehe.