This problem obviously got some attention for it to have been partially fixed in 10.11.4, unless the improvement was happenstance.
I've had nothing but Apple Computers since the MacPlus and this is the first really major disappointment in over 30 years of using their products. Years ago I started a log of every update I perform to trace problem causes, but while I still do it, the software has gotten so good over time, there were no problems. Until El Capitan.
I see no compelling reason to update my main computer, a 2009 iMac 27", I was in an Apple Store last week. The new versions have prettier screens, more cores, and are thinner. After seven years, that is it. I had an iPad, sold after I got my iPhone 6. See no compelling reason for the iWatch, newer iPads, or anything there. The best application I use turns out to be One Note from Microsoft, and it runs everywhere I go on everything I use. No sync problems ever. I gave up on Notes when the sync between my iPhone and my Mac when south. Couldn't fix it, never looked back.
I did look at the AppleStorageDrivers.kext bundle. El Capitan also came with some really irritating problems with my USB devices, including my Apple Keyboard and Mouse. I can't help but wonder if the problem is USB and the card reader is just a victim. Not that it matters.
I use Windows 7 computers at work and it used to be nice to come home to OS X. No longer. I use and wait for my keyboard to become unresponsive, my SDHC cards to not work, and other weirdness. My options remain open when it becomes time to get a new computer. If Apple comes through, I'll happily stay with them. My expectations are low after this.
The best I can report on the SDHC issue is, I can use the card for a few sleep cycles over a few days before it goes south.
It is one thing to have problems in new features, it is another to break what once worked well. That speaks of poor development practices, poor regression testing, or lack of concern over issues found.