I've figured out the running problem.
If Stamina runs out (which it tends to do once the trainer stops keeping it infinite), it completely disables running until you reload an area (e.g. teleporting to a bonfire).
And yeah, the Health is maintained at sub-full values (at least when Embered), which is a bit of a pain... and that when it works at all. HP, FP and SP stop working entirely very easily. I mean the other trainer on WeMod is wildly flakey, but it seems to reactivate itself far more often than this does.
I saw mention of some sort of anti-cheat measures in the game that the other trainer is set to circumvent... but this one seems somewhat less up-to-date and doesn't do as well at it.
Problem is though... this trainer and the other trainer achieve different things better. The other one maintains the attributes better, keeps the character weight at zero, prevents curse (alone).... while this one actually has a working drop-rate increase (good for farming enemy drops), can maintain buffs indefinitely, and prevent all statuses (but is terrible at maintaining HP/FP/SP and doesn't do the weight thing properly).
So... yeah. Trainer options for this game are a bit of a mess. Better than nothing, but hardly reliable.