Hi Michael, having built 3 kits out of Basswood I can say that on some curves or edges the stain won't take as well as in other areas and only through reapplying will it gradually accept some colour. Just the nature of the beast with this timber.
That said, it is way too easy to over sand and end up with shiny bits that tend to repel stain. If you got up to 400 grit you went too far as 240 seems to be about far enough as you can get things smoother later after top coats have been done.
If you did go too hard on the sanding suggest going back to 120 then 180 and maybe 240 but no higher.
Unfortunately this will strip most of your first stain coat but will help getting it to take colour overall.