SQL Server is running slow after a certain amount of time
I'm not sure how this recommendation will be viewed, but based on the vague nature of your problem description and report of steps you've taken, I'd recommend going with something that attempts to answer some of the 'what do I look for / at?' for you like the stored procedures Sp_blitz and sp_askbrent over at brentozar.com.  You may need to start with some basic health checks before you dig into the causes of for your performance issues on particular jobs. While this doesn't specifically answer your question, it's somewhere you can start. Brent's work is awesome and you'll find actionable output  that you will point you to potential solutions. Otherwise start with using activity monitor to see what else may be hitting the same tables while your jobs are running. At the same time check your growth patterns and see if you've had some growth recently within the tables your hitting. You may be limited in what you can retrieve depending on whether or not you're warehousing DMVs (or restarting the services for that matter) so setting of the built-in warehouse to store growth (etc) might be something you need to look into. In general if you have a solution in place to retrieve and retain DMVs you'll be able to act when problems like this come up. Sorry if I'm all over the place with this response.