Not sure what year your talking about, but my 05 grand prix has the "whos got the crack syndrome"
Theyll work fine at anyspeed, then all off a sudden they crack out, get stuck, and will only work on the high speed setting. Give it a few minutes and itll be back to normal. Its not the arm for the turnsignal and such.

Ive read that the wiring harness connections under the cowl can get soaked in water and also the linkage cant get dirt and debris on it creating this problem. both with are free to fix if you have 5 min.. id check into it before anything else. Take the connector apart and see how the pins are, coat with some dielectric grease and try to seal it up better or hide it from rain water...