If you never play the China Card, trigger all the starred Early War events but Blockade in turns 1 & 2, have the US headline "Ask Not" and discard its entire hand, and discard all five cards with "Our Man" you can get a T6 reshuffle.

Early War Cards | 38 | 38 Deal T1 | -16 | 22 Deal T2 | -14 | 8 Shuffle in Discard Pile (19 starred events [all but Blockade] triggered) | 9 | 17 Deal T3 | -14 | 3 Mid War Cards | 48 | 51 Deal T4 (Blockade & 5YP played for discards in T3)| -18 | 35 Full "Ask Not" Headline | -8 | 27 Full "Our Man" | -5 | 22 Deal T5 (Grain Sales played & drawn card played) | -17 |5

Obviously at this point a T6 reshuffle is mandatory, and I think this would lead to a T9 reshuffle as well. So, a full game of Twilight Struggle can have anywhere from two to four reshuffles!