Some researchers have reported that the skin conductance level (SCL) is mostly hovering around zero microSiemens (µS) with occasional spikes. This is most likely a sign of a loose electrode.
There are many causes for noise in signals but typically if you're E4 appears to be recording EDA properly with variable SCL above 0.5 µS and then suddenly you start seeing data that appears mostly flat (around 0 µS) with occasional spikes in the signal it can be attributed to a loose electrode.
Please try removing the E4's electrodes by hand. Replace the electrodes and tighten them as much as possible by rotating them clockwise by hand (see the article on electrode materials and replacement for detailed instructions) Try generating a new recording and see if the situation has been resolved.
If the issue is not resolved inspect the electrode connection for damage to the threading and report the trouble to firstname.lastname@example.org. Make sure to provide at least one example session URL in the report for efficient service.