I'm currently going through precisely this problem - I feel better, up the exercise and then feel worse again. In my case, my FT3 is in the basement, so every time I run my body seems to use up all the T3 I'm taking and then somehow forces my body to use some T4 (which it is generally not very keen to do). So I end up with low TSH, low FT4 and low FT3 (which isn't supposed to be possible, but there we are!)
So then I increase my dose and the cycle starts again.
I've done a lot of running in the past, so I know I'm not over-training and it's not my diet etc which is causing the problem. My ferritin etc are all ok, so I'm convinced that exercise uses up thyroxin, in a major way.
My hope is that eventually I will find a dose which allows me to exercise without the crash. My situation is complicated by being a thyca survivor who is on TSH suppression, so I'm not operating within normal ranges anyway.
So far I've added 25mcg of T4 and 5mcg of T3 to the mix - the extra T4 made only a little difference to both my blood tests and my energy, so we can only hope that the extra T3 will help.
I'm trying to look on the positive side - at least I actually feel like running, for the first time in years... I'm determined not to give up.