I experienced this today, very frustrating; sendmail all locked up and outputting this bizarre “timeout waiting for input from local during Draining Input” error into the logs.
tl;dr: figure out what sendmail is waiting for.
In my case, it was stuck on procmail. But why? Turns out the local mailbox (a user that runs a lot of crons) had hit 3GB, at which point it didn’t seem to be accepting any more email into that inbox. Moving that file out of the way and allowing a new one to be created caused the queue to be flushed instantly.