9v & 2 high power LEDs | LEDs dim after time, bright again after being off
It's a combination of a few things. 9v batteries are low capacity batteries designed for small current draws over a long time. Due to their chemistry, typically multiple 1.5V alkaline cells or piles, they have a high internal resistance, and as more current is drawn, the bigger the voltage drop across the battery's internal resistance. Just like the leds and the resistors, this internal resistance varies based on the temperature it is at, and high current draw will cause it to vary causing your device/leds to see different currents too.

Add to this, the voltage recovery effect seen in batteries, where energy in a battery that has experienced a high discharge takes a while to distribute within the battery chemistry. At the discharge rates I calculated (~300 mA) it will only last about 2 hours anyway, regardless of recovery. As the voltage drops, the discharge rate changes, but the useful life is low for what you want to do.

In short, high current draw is not good on 9v batteries and the recovery effect you see is a side effect of it.