Sounds like the solenoid is shot. Sometimes these are just bad from the factory, I replaced my stock starter (for the same exact reason) with a rebuilt one from Kragen and had it die within a week. They replaced it, but its not uncommon with the new electrical stuff. On a slightly different note, I went through about half a dozen condensers on my Austin Healey before getting one that worked. Manufacturing standards in China aren't all that great, and if there's a flaw the insulation breaks down under heat and causes the non-starting issue. Once cooled it works again, but as you know only until it gets hot.
I believe you can just get a solenoid for the mini-starters, that way you wouldn't have to replace the whole thing.
