"How do I avoid podcast audio from stop playing on iPhone as the screen turns off?: I just started having this issue. When listening to a podcast the audio stops when my screen turns black.. it never used to ... or maybe my screen never shut off while listening. How can I get my screen to stay on or my audio not to stop??!!!"
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What is your iOS? Updating it may fix this.
Go to: Settings > General > About
So, Update the iOS Using a Computer:
Plug you iPhone into a computer > Force restart the iPhone > and then complete the update using the computer. Use my User Tip: Update your iPhone Using a Computer - User Tip
For Future Reference...
IMPORTANT: If you have an option to update, however, then be certain you backup your iPhone first. That way, you will have something to restore your iPhone from should anything go wrong with the update