Typically, this is how I get my best consistency, though certainly never for that long. Most I've gone has been maybe 6-7 months. Expect to go everyday. This is why I train with Hansen's marathon training, because it's 6 days a week, which is much better for me since it's a habit and it feels weird when I have a day off, instead of taking many days off.
Running
A place for runners.
That's an amazing streak. Congrats on keeping it going!
Streak running was exactly what got me over my initial barrier back when I was struggling with recurring injuries in beginner-level marathon training plans. I think the consistency of those easy runs really built up a foundation for more focused training in a way that the on/off schedules couldn't. I dropped the initial streak just before finishing a full year, but I have a feeling I'll circle back eventually when I'm running just to stay active instead of training for specific events.
I tried that back when I was only getting into running. If I recall correctly, I kept it up for a little over a week before I overloaded my achilles heel and had to stop running for a month. Since then, I'm only doing occasional shorter streaks, e.g. when on organized runners' camp or retreats.
Running every second day is easier for logistics, especially the laundry! :)
Preach on! I've crossed my 3 year mark in April, and I had exactly the same experience as you: once it's a habit, motivation is secondary, good discipline regarding slow recovery runs, and I also had some weird runs. Including the one where I ran around the hospital while my kids were waiting inside, with their mom. It was 11PM, we've been waiting for 7 hours at that point, and I had office clothes and shoes. It was snowing outside, but I had to feel the parking meter again, so I made it a quick run, just to keep the streak alive.
I'm not a streak runner, but I have kept up a 4-6 days per week habit for the past two years. I have been surprised by the benefits that come from keeping up with the training through the cold months. E.g. I dropped 15 minutes from my half the first year and another 10 minutes the second. But the biggest benefit is similar to what you said about motivation and discipline. I just don't struggle with it any more now that running is a year round habit.