Try training in... Driving & Harness work (x6) which I think is the strength equivalent of halter and see if it will force the Str to red cap. Good luck. fm
It goes down? Double check your diet. Str only goes down if it somehow equals less then 100%. I did this accidentally once when I set it to 02/15/50/15 instead of 20/15/50/15. Wretched typos! fm
I think there's some kind of glitch going on. I haven't yet reported my own case to Nef, but yours sounds the same as mine, only with the Strength stat.
It's frustrating, I know.
I wish I knew what to tell you to do, but I don't. I thinked I lucked out with firemedics help.