When your tournament is in a 'checking_in' or 'checked_in' state, there's no way to edit the tournament's start time (start_at) or check-in duration (check_in_duration). You must first abort check-in, then you may edit those attributes.
POST
https://api.challonge.com/v1/tournaments/{tournament}/abort_check_in.{json|xml}
| Name | Description | 
|---|---|
| 
 Required 
api_key
 | 
Your API key (required unless you're using HTTP basic authentication) | 
| 
 Required 
{tournament} (in URL string)
 | 
Tournament ID (e.g. 10230) or URL (e.g. 'single_elim' for challonge.com/single_elim). If assigned to a subdomain, URL format must be :subdomain-:tournament_url (e.g. 'test-mytourney' for test.challonge.com/mytourney)
 | 
include_participants
 | 
0 or 1; includes an array of associated participant records | 
include_matches
 | 
0 or 1; includes an array of associated match records |