I guess on where you purchased the starter, to me that is not the major problem. All locations mentioned have sold me perfectly good working parts. While I prefer Carquest or Napa I have bought plenty of parts from Autozone, Reilly's and Pep Boys. The problem is mostly as some one said, a rebuilt starter can do exactly what you say is happening. When you deal with rebuilt or used parts (junkyard) that is the gamble you take for availability and price.
Been there, done that for 55 years. And quite frankly a lot of those stores get there rebuilt replacement parts from pretty much the same people.
So bite the bullet and pull the thing, take it back where you bought it from have it tested and insist on a replacement.
Will that solve the problem? Probably!