Welcome to the BA forum on Flyertalk.
I've seen a number of reports of this, and I suspect it is caused by some cookies interfering with the process. Among the solutions are
- use the App rather than your PC / tablet, or vice versa
- use a different browser
- Try incognito / InPrivate or other special access mode of your browser
If it's for a particular booking, you best log out of BAEC, then use name and PNR to change the API data in the Manage My Booking area of the booking in question.
Don't worry too much, it happens fairly frequently so you can do all of check-in at the airport if necessary, just add a little extra time for this.