Spector's attorney, Bruce Cutler -- whose health issues resulted in Monday's court session being canceled -- said he was having problems with his diabetes medication, The Los Angeles Times reported Wednesday.
The iconic music producer has pleaded not guilty in the 2003 death of Clarkson, who was found shot to death in Spector's Alhambra, Calif., home. If convicted, he could face a prison sentence of up to 15 years to life.
While testimony was postponed, lawyers Wednesday were preparing to argue a prosecutor's motion that accused the defense of submitting forensics evidence late.
In a response filed Tuesday with the court, the defense denied it intentionally delayed giving prosecutors blood-spatter test results that suggest Spector was at least six feet from Clarkson -- who was shot in the mouth -- when she was killed.
The evidence could be crucial to determine whether Spector shot Clarkson, as the prosecution claims, or whether the actress pulled the trigger in an "accidental suicide," as the defense maintains.