2,000 watts of lighting, sounds like an 8x10 enlarger.
I don't know what you call long exposures, but in my book a long exposure is one where you set the timer in minutes, something like 5 or 7 minutes for an exposure. This is for mural enlargements using a 10x10 horizontal enlarger.
With a conventional vertical enlarger with 2,000 watts of go juice, unless you were enlarging with a 380 or larger lens at f64 or so, I wouldn't expect anything longer than about 25 seconds, 45 seconds tops, for the size of enlargements you are talking about.
Yes, the lights can go out, when one goes you do have to replace the whole 8 globes.
I would suggest with your reasonably short exposures for a 2,000 watt head, you may be getting minor colour changes due to lamp temperature fluctuations.
The best 2,000 watt tungsten head enlargers, always had a shutter in the head. That way the lamps stay on permanently (so to speak) and when you press the button your integral timer trips the shutter and away you go.
If you place a quite sensitive light meter under your enlarger, place some extra diffusion material above the sensor, then trip your enlarger in total darkness and watch the meter change as the exposure ticks on towards a minute.
I have the original Jobo Colorstar analyser made by Lici, it has a digital readout and I know that a powerful colour head will still be warming up for the first 5 to 10 seconds. In fact all tungsten lamps do, but with a power source as you have the effect can be noticed by paper more easily, than with a single tungsten lamp enlarger
Mick.