I can confirm this problem since I updated to Kitkat (4.4):

Downloaded Feeds
Downloaded Episodes
Failed Episodes
Title: 28112013 - Löffel im Glas
Reason to fail: IssuficientStorageSpaceException - Unzureichender Speicherplatz um den Download abzuschließen! Erforderlich: 2 MB (needed 2 MB, my phone has 8.45 GB free!)


Feed Update Details

No feeds were Updated
Feed Processing Details

There were no feeds to check for new podcasts
Feed Download Details

Failed - Löffel im Glas
Feed Url: http://www.ndr.de/podcast/podcast2958.xml
Episode Url: http://media.ndr.de/download/podcast...-0656-5842.mp3
Downloaded: 0, starting at position: 0 took: 600 mSec. at 0,00 KB/Sec
Content Size: 0. Cache Size: Not Set
Content Date: Unknown. Cache Date: Not Set
Feed has Image: Yes, image downloaded: Yes
Content Compression: Not Compressed
Reason to fail: IssuficientStorageSpaceException - Unzureichender Speicherplatz um den Download abzuschließen! Erforderlich: 2 MB
Device Network Connections: "drahtlos5" (WIFI)

Background data Allowed
Environment Info

DEVICE: LGE Nexus 4 (occam) with Android 4.4

DEVICE STORAGE

• SD Card Root: /storage/emulated/0
• Cached SD Card Root: /storage/emulated/0 (autodetect root, keep missing episodes)
• External SD State: mounted
• BP location on SD: /storage/emulated/0/BeyondPod, Exists: true
• BP will use: /storage/emulated/0/BeyondPod
Free space: 8,45 GB


BATTERY INFO

• Status: 3
• Level: 83
• Plugged In: 0
• Is Charging? false
• Is Plugged In? false


FEEDLY INFO

• Logged In: No
• Has User: No
• Can Re-Log in: No


APPLICATION INFO

• Playback Speed Enabled: Yes
• CDS Enabled: Yes

This happens for all feeds! Right now BP is useless for me, as I cannot download any feed.