When the battery (~1 year old) on my 2000 Blazer was run down to 12.1 Volts (~25% charged) it started having driveability problems. The idle was ~150 rpm higher and the torque converter lockup was not engaging. When the battery was fully charged (12.6 Volts) the truck ran fine. My guess is that the VCM (computer) needs a minimum input voltage or it gets a little flakely.
Ed B.