Is there any valid reason to ever ignore a caught exception

Question

Wow, I just got back a huge project in C# from outsourced developers and while going through my code review my analysis tool revealed bunches of what it considered bad stuff

Answer 1

We have an application that does a lot of processing on behalf of other applications, where you insert some job (collection of config) into a database and the app will take it and run it at the appropriate time. We tend to swallow a lot of exceptions in that application, because even if Job1 dies in a horrifying fashion with a catastrophic error, we want the app to stay alive to take a stab at processing Job2.