Does she get fed after her workouts? Untacked and immediately turned back out with friends?
Horses learn the routine if it's set. If the routine changes suddenly, they will react accordingly.
I would suggest after your next session to untack, putz with her for a bit and then retack her up. Even if you just lead her back to the riding area - it's a change in her routine!
Spot on! I couldn't have said it better myself!
If she knows that when that saddle comes off she is going to get plastered with treats and love and put back with her buddies, she is going to be aching to get that saddle off and get some yummies into her stomach! I've admittedly had to cut the cookies with my guys because they became to expectant of them (I made sure to stop -before- they started pawing or pacing around their tie). They would get agitated whenever it took me a while to go into the tack room, because they knew when i came out i would have something nice for them.
Anywhoo.. as mls said, change the routine up! Take the saddle off and poke around on her bareback (with helmet please!!) and just enjoy her company. Then put the saddle back on. I would even go as far as to say that when you go to untack her the moment the jigging behavior starts, re-tighten the girth, drop your irons, and hop back on and walk a lap around the arena. Lather, Rinse, Repeat.. so to speak :p continue this until she has calmed down then untack her.
(Edited to add: Oops, i see Vida already touched on this!)
Change the scenery when you untack her.. that may help too. Maybe even try untacking her inside the arena and letting her roll right after a ride. My guys always love that! Mmm Arena sand + sweat = Love!