you may consider to try the system out with another non-futaba servo, if the probem goes away, then probably the Hitec servo has probem.
3pks is a very smart transimitter and it can automatically change the mode by itself.
Your problem more sounds like a faulty servo which easily overheats(towards the end of the play)
That's the reason why I often discourage people from buying these third party servos. A little bit cheaper, but creates a lot of problems and takes away your fun. It doesn't worth it.