You can absolutely patch a runflat as long as you haven't driven on it with no air pressure in it. If you have a nail embedded and have a slow leak, its perfectly fine to repair it. The sidewalls get damaged if you lose all pressure and then it's irreparable. A lot of shops just refuse to repair them because they don't know if you drove on it without air in it. It's a liability thing.
My tire were slow leaks. Like if I fill it back up to 45-50 psi, it will slowly leak to something like 20-30 psi in one day. When I had to do a trip from Orange County to San Ysidro (San Diego / Mexico border) rount trip about 180-200 miles, I put air in my tire before going on the freeway and starting my trip because it was low. But it lasted the entire day just fine.
And some days I just kept driving even when it got low to 20 psi, but that's why I decided it was time to take it in after 1-2 weeks of low tire. I never felt the tire become wobbly, just an annoying warning sign.