what's causing a SME 3 to stick after a few spins?

That sounds right but when I lower the arm in the space between the arm rest and the platter it drops a few mm below the lp surface. Thanks anyway

The problem occurred when I first hooked up the turntable after arriving from Fed Ex. It eventually improved and then returned after I adjusted the overhang. This mis-tracking went away also and now seems to be working just fine.
By skipping I mean it gets stuck in the same groove. When I raised the arm and and gently pushed it towards the spindle I did feel a little bit of resistance.
I'm not the first owner and the person I bought it from wasn't either but says it was set up professionally.
I'm going to change the cartridge and see if the problem returns.

"Luckily" after playing through 3 sides without incident this morning I got stuck in a groove on the first track of the 4th side. I found some thread, looped it around the arm like you said, lifted it up off the lp and tried to move it toward the spindle. I definitely felt some resistance where it was stuck and once I moved it past that point it was moving fine.
The cartridge, by the way, is a nearly new Rega Bias 2 tracking at 1.75g.

The only response I got was from SME simply stating that they don't support the series III anymore. No one else responded including a couple of other companies I came across.

The only thing I have to add is that while working on the motor of the Rega I had it turned upside down. When I flipped it back over the arm would get stuck immediately as opposed to after a few revolutions. I moved it back to the work bench and suddenly it felt free with no resistance. I reconnected the table to the amp and now it seems to work just fine.