Ever open up your rear gate, and look down to the bottom left rear and see an oval hole with no plug in it? (Same size hole as on the right side, but the right has a plug.)
Well, there is a cure...

Subject: Info - Availability of New H3 Back Body Opening (D Pillar) Plug for Service Replacement of Loose/Missing Plug #06-08-66-007 - (04/20/2006)

Models: 2006 HUMMER H3

Here is the new part number:
15855927 - Plug-Bk Body Opg Lwr Frm

Yes, those started popping out the first day. I put it back n a few times and then eventually lost it somewhere. I was going to silicon it in place but it was gone before I knew it.

I checked mine today .Both of them are in there tight.