I've seen ground stakes made specifically for cameras with GoPro style mounts, but they all assume they'll be going into soft dirt. As anyone who's ever pitched a tent can attest, this isn't always the case.
Pounding on thin tabs isn't the best way to get something to stick without breaking stuff... This is a way to get around that.
Step 1: Materials Needed
Rummaging around and cleaning things up as per my wife's request, I came across a set of well used tent stakes. I don't remember where I picked them up, but the tag tells me they were distributed by Big Rock Sports of New Bern, NC U.S.A. They're old, but well made and may very well still be available.
The only other things absolutely needed are one 10-24 or 5mm acorn nut, the STL file above and access to a 3D printer.
Step 2: Assemble
First, cut the hook off of the stake and sand or file the upper portion so the sides are parallel.
This next bit is optional. Enlarge the diameter of the stake's hole to allow a thumbscrew's threads to easily pass through. I used a 17/32 bit, but any close size should work.
Using a suitable sized soldering iron, melt a 10/24 or 5mm nut to one side of the hole. My Weller is among the missing and one of the reasons for my wife's suggestion, so your results should look better than my hacked attempt.
The thumbscrew you use doesn't have to look like mine, with its plethora of spacers as I show won't be necessary. This was my first and only print and I neglected to add a second hole to it. The stl file has corrected this, so the thumbscrew doesnt have to be a specific length, as as long as it can reach the distance to the nut.
Finally, press-fit the acorn nut into the corresponding tab and fit the cap onto your stake.
Step 3: Use
If the cap fits as snugly as mine, you might carry the parts press-fit assembled and omit the thumbscrew, enlarged hole and soldered-in nut altogether.
Now, when faced with a stake setting situation that needs a bit of persuasion, remove the cap and pound away.
Hope my ideas help instill some creative thinking in the GoPro Instructable community.