Using a constant sample concentration and injection volume (20 uL), what could cause my peak area to vary with flow rate?
The peak area is always largest at 0.5 mL/min, and progressively diminishes until it levels off between 1.5 and 2.0 mL/min.
Could this be an instrumental problem, or a chemical effect (slow analyte desorption) ?

Neither. There is probably nothing wrong with your system.

You're integrator measures peak area on a time basis (e.g., mV-minutes). Peak area will only remain constant on a volume basis (e.g., mV-mL). Correct your peak area to a volume basis by multiplying by your flow rate.

If the peak area on a volume basis doesn't remain constant, then check your flow rate by collecting in a small graduate and timing with a stop watch.