Long term storage of sp_server_diagnostics results
No, but as MS recommends, you should save this off either to an external file via Extended Event or log it to a table.

Taken from sp_server_diagnostics:

-- Create the Event
CREATE EVENT SESSION [diag]  
ON SERVER  
           ADD EVENT [sp_server_diagnostics_component_result] (set collect_data=1)  
           ADD TARGET [asynchronous_file_target] (set filename='c:\temp\diag.xel');  
GO  
ALTER EVENT SESSION [diag]  
      ON SERVER STATE = start;  
GO  

-- Read Output
SELECT  
    xml_data.value('(/event/@name)[1]','varchar(max)') AS Name  
  , xml_data.value('(/event/@package)[1]', 'varchar(max)') AS Package  
  , xml_data.value('(/event/@timestamp)[1]', 'datetime') AS 'Time'  
  , xml_data.value('(/event/data[@name=''component_type'']/value)[1]','sysname') AS Sysname  
  , xml_data.value('(/event/data[@name=''component_name'']/value)[1]','sysname') AS Component  
  , xml_data.value('(/event/data[@name=''state'']/value)[1]','int') AS State  
  , xml_data.value('(/event/data[@name=''state_desc'']/value)[1]','sysname') AS State_desc  
  , xml_data.query('(/event/data[@name="data"]/value/*)') AS Data  
FROM   
(  
      SELECT  
                        object_name as event  
                        ,CONVERT(xml, event_data) as xml_data  
       FROM    
      sys.fn_xe_file_target_read_file('C:\Program Files\Microsoft SQL Server\MSSQL13.MSSQLSERVER\MSSQL\Log\*.xel', NULL, NULL, NULL)  
)   
AS XEventData  
ORDER BY time;


Alternatively you can log it to a table:

CREATE TABLE SpServerDiagnosticsResult  
(  
      create_time DateTime,  
      component_type sysname,  
      component_name sysname,  
      state int,  
      state_desc sysname,  
      data nvarchar(max)  
);  
INSERT INTO SpServerDiagnosticsResult
EXEC sp_server_diagnostics;