SSRS Subscription Error Message :Failure sending mail: The operation has timed out.Mail will not be resent

Following are the suggestion(s) which may not be solution but we can try if you are pulling all the data in single page and it is tabular report.

1) Check the Query in SQL Server and optimize it. (if Source is SQL).
2) If in case, Query is fine then check at report definition.
3) For testing purpose, try to use page break.
4) Adding page breaks can improve the performance of the reports because  processing of full report & page break report is lttle different.  
5) SSRS process each page one by one in case of page break.
6) Displaying all data on a single page will typically result in a performance issue. 
7) In full report processing, report will not generate until it completes the report processing. Sometimes, it got time out.
8) Instead, use page breaks to display the data.

Hope this will help to resolve the issue of report processing using email subscription.