If you observe a sudden drop in current, the problem could be due to a particle causing a blockage in the capillary. If this occurs, try flushing the capillary with filtered, CE-grade DI water. To do this, simply inject the water into the capillary with a proper syringe. Inject in the reverse flow direction because particulates are more likely to get stuck near the capillary inlet, making them easier to remove from the reverse direction. The inner diameter of the capillary is small enough such that even small particulates can cause a blockage.
The pressure applied should be enough to dislodge any particulate matter that may have caused the blockage. It is important in CE to ensure all buffers, water and samples are thoroughly filtered prior to introduction to the instrument.