Rust and corrosion on the threads causing the nut to be extremely tight coming off. The spindle can only take so much force before it breaks.
Stripped spindle/splines, linkage issues.
Check linkage first and stripped or loose wiper arm on spindle.
Check your wiper linkage under the hood and/or the tightness of the wiper arm on the wiper spindle.
Check your wiper linkage and/or the splines on the spindle.
Usually, the arm. It loses its springiness/pressure against the window. The spindle is lubricated and most vehicles NEVER have a problem. The only issue that may develop with a spindle is someone 'hammering' the arm on or not mounting the arm fully down on the spindle. Then the ridges on the arm get damaged.
Either the wiper arm(s) moved on the spindle or the linkage moved or bent. See sources and related links below for wiper blade information.
You can change the wiper blades by removing the retaining clip to the wiper blade arm. The wiper blade will come off and can be replaced.
In many cars, there is only a single wiper motor. One wiper arm is attached directly to the wiper motor and the other through a linkage. If one is working, the motor is operating but the connection to the other may be broken.
Begin by removing the wiper motor wiring harness. Remove the traveling arm linkage retaining bolt. Remove the wiper motor retaining bolts. Reverse the process to install the new wiper motor.
The non working wiper on the 2001 Century most likely has a broken wiper linkage. The linkage can be checked by removing the vehicles cowling.
1998 Mercury Mountaineer rear wiper troubleshooting - check in this order: Fuse, switch, spindle/tightness of arm, motor, wiring. See the Sources and Related Links section below for rear wiper blade information.
2003 GMC Envoy rear wiper troubleshooting - check in this order: Fuse, switch, spindle/tightness of arm, motor, wiring. See the Sources and Related Links section below for rear wiper blade information.