Why is there a several hour delay in getting emails from another account?

Up until a couple of weeks ago I would instantly get emails from another account. Its work related so quite important to me. However now, there is a delay of several hours. It started off as a 24 hour delay so I deleted the account and set it up again. It improved, but there is still a big delay. Can anyone indicate as to why this has happened and how to rectify it? I have been in touch with the service provider of the other account and everything there is working as it should. They said it was a problem at the receiving end. Thank you....