Peter Pumpkin was stolen from the Neat Marsh Road area of Preston at around 11.30pm on Saturday, July 17.
The pony is chestnut in colour with two distinctive white markings on his face and is around 40 inches tall.
Peter Pumpkin requires daily medication and police are concerned that the current heatwave will have a detriment to his health if he is not located soon.
Sergeant Julie Fenton from Humberside Police said: “Peter is a much loved and adored pony who has been in his owners family for 31 years. Understandably, they have been left devastated by this incident.
“They have been over-whelmed by the help and generosity of the public so far with searches and information, however we are continuing our appeal.
“We are keen to trace the people responsible and reunite Peter with his rightful owners.”
Officers are currently following a number of leads however they are still appealing for anyone with information, or anyone in the area of Staithes Road or Neat Marsh Lane, who has not yet spoken with them to contact the force on 101 quoting crime reference 16/72507/21.