Your 1600 time is almost exactly 16x your 100 time, so I don't think you need to work on your endurance nearly as much as your speed. Like ston-ar said, go short. I'd even venture to say that repeat 100s at or near lactate will be one of the most beneficial things you can do right now. Keep doing everything else, though (distance, drills, etc), just add a lot more speed work.

Do them on an interval. You want them to be as hard as you can go (with good form) while maintaining pace with a short rest. For example: 10x100 on 2:15, holding 2:05 for each (10 seconds rest).

My coach keeps telling me that I get flat once I get tired. Thus the big drop off from a 1:44 100 down to 2:04 100s as they add up.

I think part of the problem is I'm not fully aware of how to drive that rotation. (when I'm fresh it just happens, ya know?)
It seems once I'm tired the next thing he tells me is that I'm trying to rotate from the shoulders and that's not going to work.

Am I going about this the wrong way? Is there something else that I should be working on, or thinking about, that would help me keep my rotation from the hips? Or are we on the right track here with building speed/endurance?

Thanks for sticking with me on this one.

It is a good start but once you start feeling good about your swimming you have to up your workouts.

A weekly combination of - Max VO2, Aerobic and Aenerobic swimming works good. If you only swim 3 times a week 1 day of each type is good or if you swim 6 days a week 2 days of each type of work out. Never do more then 2 Max vo2 workouts a week.

It sounds to me like your muscle memory with good technique is still not solid. It takes awhile to be able to move from using good technique in drills to be able to using it within your regular sroke to using it continuously for a long time. Swimming especially uses so many different muscle groups that this process can take time. The muscles necessary for that good technique need to be strong enough to keep the technique solid for longer and longer distances. Until you've built that technique into your muscle memory, I wouldn't swim any longer than you can hold good technique for.

I don't know how old you are, or whether you're male or female (one good reason to put basic info in your profile), but assuming you're not over 50, then a :44 for a sprint 50 and 1:44 - 2:04 100 times would suggest to me that you can still be working on technique as your primary focus.

What I like to have my swimmers do is one 25 of focus on technique via a drill, then 50 yard swim trying to hold that aspect of technique. Do these as repeat 75s. Once you can hold the technique for the entire 50, up these to 25+75, then 25+100, and so forth. The drill 25's are to re-focus you on the aspect you are trying to improve. Keeping the rest of the interval short allows you not to fatigue into poor technique.

Swimming is so much more about good technique than it is about endurance and fitness. It's hard for many athletes to let that one sink in, but it's true. I swim with 65 year olds who can hold 1:20 for 100's, and their endurance and fitness levels are far below that of a 30-something year old swimmer. It's all about technique.

Finally kicked my cold and I'm back training again.
I did 10x 100s on 2:15s the other day and I really focused on my form. I think my worst 100 was 1:55ish (could be because I was so fresh from being sick, if that makes any sense).
Here is what I feel may be part of my "problem".
My first few 100's I'm able to keep my forward lean which keeps my hips & legs up. As I fatigue, I think I have trouble maintaining that forward balance, Which then drops my hips and legs, thus my being slower.
I feel my balance could be changing because of my breathing. When I first start I keep my chest very open, which helps with my buoyancy. I guess currently I can't maintain that. My question is should I be trying to "hold" my chest cavity open as I do? Or is that just something that is just wrong.
I guess for as much as I swim, I don't have a clue as to what the "Ideal" breathing cycle should be and how it should feel.

Kind of long winded...Hope my question makes sense to someone out there. Thanks in advance.

Good Call Ston_ar.
I was definitely holding my breath, then blasting it out in time for the next breath. (horn player, strong lungs....). Obviously that is not good for swimming. I need to work on exhaling at a much more relaxed pace, continuously, as soon as my face is back in the water. I don't think this will be a hard adjustment. Just need to keep focused on it for awhile.

Here is another question. When we do 25yd no breath drills, do you still exhale the same way? Slower?

I appreciate all the feedback. I've been doing the 100 repeats as a mainset. Then a few sprint repeats after the main. I need to work ironmom's Drill/swim 25/50 into my plan, that just makes good sense. The VO2 Max workout has been the 90 min masters swim each week.
I also just watched a ton of swim videos on You Tube. I needed to see this High elbow catch to help me visualize that.
Thanks again. I'm off to the pool.

3 seconds per 100y is close to a minute dropped from your 1 mile time....a very significant improvement! Congrats and keep up the hard work.