A plug inserted from the outside is often cut by the reinforcing belts in the tire (the ones you had to core out) and that is when the plug fails. It is a low quality repair best suited for nylon belted bias ply tires. Works fine on those.

A proper repair is done with an inside patch.

A proper repair for a runflat tire is a special inside patch that is a combination of a plug and patch. It looks like a mushroom, and the stem is pulled out through the hole in the tread when it is installed. Of course, the tire is demounted and the gluing area is roughened up and then cleaned first.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue