03 Oldsmobile Silhouette 3.4L Starter stays engaged at times.

Sounds like time for a new starter. While it could be electrical, in that the starter circuit is remaining engaged, more than likely it is mechanical. As the starter wears, you get play in the starter gear. Replacing the starter should take care of it. If you have recently had the starter off or replaced it, it could be misaligned, causing a similar problem.

Is it possible the there is a problem in the ignition switch that keeps the starter engaged, although I would lean toward a starter problem? Just wondering.