I used to train at the gym 1.5 hrs 4-5x/week in my late 20's and was a nationally ranked lifter and bodybuilder. In 2001, I got hit by a car and after a bunch of surgeries, was tired, achy, & bedridden for a long time, but was back in the gym for rehab in 2007.
I figured out I had CFS when working out at the gym for an hour a 2-3 times a week always made my fatigue worse instead of better. I quit right after getting a national Masters (50+) Bench Press record and elbow surgery in 2011, but then started back once a week a year later. I retired from my job in 2014 when my fatigue was so bad I had a hard time making it through an 8-hour day.
I then I took up bicycle riding last year (2015) 3 months after another surgery (& thus flare up of CFS, again). I somehow also gained 25 lbs in 6 months, while eating only 1600 cal/day, low-carb. My heart rate would jump to 165 after going over an overpass on my 3 mile route, and not come down for 30 minutes. EKG, T-wave, chest Xray, etc were all normal. I started to ride the Lifecycle at the gym, keeping my heart rate low (110-120), and building up the miles for a few months, then eventually built up the miles outside. Now I can do 25-32 flat miles at 12 mph average with my morning riding club (a bunch of retirees 55-87 years old) 2x/wk, but doing more lays me up for a week instead of 2-3 days. I am just totally fatigued head to toe, but the legs don't ache at all since the riding itself is so easy for me, strength-wise.
I can not seem to progress past that level after 9 months of trying; My heart just goes too fast (165-178 bpm) on even minor 2% grades, leaving nothing for the hills.
My cardio training books say it is normal to progress about 10% a week when starting out, so if you can ride 20 miles, then you should be able to do 22 the next week, and so on, which sounds reasonable. It worked for one month, then stopped. My 290 lb non-CFS friend was able to lose 30 lbs and ride 100 miles in 3 or 4 months, at age 63.
Nothing in my cardio training or CFS books addresses mid- or advanced level cardio training with CFS/ME, once PAST the Don't-Want-to-Get-Out-of Bed phase.
Good News is that in the month since I started on the D-Ribose in my coffee, etc., I am now sleeping 5.5 to 6 hrs a night instead of 3.5 to 5, and need only 2-3 days to recover between flat rides instead of 3-4. My cardio fitness goals are to do 1) hills with names, 2) a century and 3) multi-day ride someday.
With CFS, I have no idea if it is possible for me.
An electric bike, or a motorcycle, is one solution, but plenty of low HR (60-70% VO2 max) training 'as tolerated' with 1-3 days in between and frequent breaks is the better solution, per my research so far.
You're quite right, most GP's dont even consider it - 
