Returning ssis errors to sql queries
Try SSIS Logging:

You can use SSIS Logging for your SSIS package to push your errors to places you can monitor them. For example, we use SSIS logging to push our SQL maintenance errors to a local database/server, to a remote database/server, and also to a CSV file on a file share as shown in Figure A. 

The SSIS logging that get's piped to SQL Server goes to a system table it creates in the database of your choosing called dbo.sysssislog. Once errors are piped to the sysssislog SQL table you can query it directly to check for errors using VS. (sysssislog is too raw a format for me personally. I parse this table to another table that has less and yet more meaningful information via a SQL Server job).  

Or alternately, you can use SQL Server mail to continually check the sysssislog table and e-mail or text you if there's an error. If it's relatively low priority but needs to be reviewed, you could create an SSRS report to periodically review the data in the table. This won't fix your error, but at least you'll become more aware of what's going on and maybe give you more information you can use to find the actual underlying issue.

Figure A: SSIS Logging Example--SSIS execution information gets piped to a local database, remote database, and a CSV file.



Note:

From the testing I've done, I've noticed SQL/SSIS has issues if I actually delete the dbo.sysssislog table. So, instead I truncate that table instead of deleting it. Before you accidentally delete this table, make a copy of the schema first--in case you have to manually recreate it.

p.s.

Not knowing your situation, you may need to wrap your multi-point transaction within the distributed transaction coordinator (MSDTC or DTC). That way, if one part of your transaction fails between SQL Server, The web server and SSIS, the whole transaction is rolled back.  Here is an entertaining (and hopefully useful) example(s) using DTC. 

https://www.mssqltips.com/sqlservertip/3272/example-using-web-services-with-sql-server-integration-services/

http://blog.arjanfraaij.com/2010/11/enabling-distributed-transaction.html