Order By causing my query to run really slow

I have an sql query as follows

select *
from incidents
where remote_ip = '192.168.1.1' and is_infringement = 1
order by reported_at desc
limit 1;

This query at the moment takes 313.24 secs to run.

If I remove the order by so the query is

select *
from incidents
where remote_ip = '192.168.1.1' and is_infringement = 1

then it only takes 0.117 secs to run.

The reported_at column is indexed.

So 2 questions, firstly why is it takings so long with this order_by statement and secondly how can i speed it up?

EDIT: In response to the questions below here is the output when using explain:

'1', 'SIMPLE', 'incidents', 'index', 'uniqueReportIndex,idx_incidents_remote_ip', 'incidentsReportedAt', '4', NULL, '1044', '100.00', 'Using where'

And the table create statement:

CREATE TABLE `incidents` (
  `id` bigint(20) unsigned NOT NULL AUTO_INCREMENT,
  `incident_ip_id` int(10) unsigned DEFAULT NULL,
  `remote_id` bigint(20) DEFAULT NULL,
  `remote_ip` char(32) NOT NULL,
  `is_infringement` tinyint(1) NOT NULL DEFAULT '0',
  `messageBody` text,
  `reported_at` timestamp NOT NULL DEFAULT '0000-00-00 00:00:00' COMMENT 'Formerly : created_datetime',
  `created_at` timestamp NOT NULL DEFAULT '0000-00-00 00:00:00',
  `updated_at` timestamp NOT NULL DEFAULT '0000-00-00 00:00:00',
  PRIMARY KEY (`id`),
  UNIQUE KEY `uniqueReportIndex` (`remote_ip`,`host_id_1`,`licence_feature`,`app_end`),
  UNIQUE KEY `uniqueRemoteIncidentId` (`remote_id`),
  KEY `incident_ip_id` (`incident_ip_id`),
  KEY `id` (`id`),
  KEY `incidentsReportedAt` (`reported_at`),
  KEY `idx_incidents_remote_ip` (`remote_ip`)
)

Note: i have omitted some of the non relevant fields so there are more indexes than fields but you can safely assume the fields for all the indexes are in the table