First, I want to note that this problem is being discussed elsewhere, though none of them provide a solution:
https://openradar.appspot.com/23222411
https://discussions.apple.com/thread/7296308
https://discussions.apple.com/thread/7318604
https://www.reddit.com/r/OSXElCapitan/comments/3wczrk/spotlight_eating_the_first _letter/
I too have this problem. I've spoken with three senior advisors with Apple Technical Support, none of them had a solution. I have this problem on both of my computers (both 15" MacBook Pro Retina). The problem arises most commonly when I spotlight search for "Things" (which is a todo list program); the subsequent spotlight search then loses the first letter that is typed. It seems like the problem arises after Spotlight does a certain kind of search.
I did a complete erase and reinstall of OSX. At first the problem was gone, but as I reinstalled software the problem came back. One time I observed that it came back as soon as I reinstalled "Things". However, another time I did an erase and reinstall of OSX and some programs (but not Things), and the problem recurred.
Given how relatively uncommon this problem seems to be, but some of us have had it on multiple computers, suggests to me that it is some software or setting that we have that has contaminated both computers. If I had the time I would repeatedly do erase and reinstalls to try to isolate what programs make the problem come back.
Any other ideas? Apple?