Some people in the town say they have not received any post since before Christmas.
People in Partridge Green, Rudgwick, Rusper, Barns Green and Faygate are also reporting problems.
A spokesman for Royal Mail said that seven postmen were currently off work at the Horsham delivery office after testing positive for Covid-19 and that other offices around the country were also affected.
Royal Mail Delivery Office, Horsham
Many people have taken to social media to query what has happened to their post describing the situation as ‘a bit worrying.’
But most are sympathetic to the postmen and grateful to them ‘for delivering in all weathers.