Current decreases while reading
You DO NOT EVER connect an ammeter directly across a power supply - the ammeter is very low resistance - essentially a short circuit - so the power supply will deliver as much current as it can - possibly damaging the power supply or the meter.

You say the power supply is rated to provide up to 1 Amp, but it provides 2 Amp when the meter is first connected.  That 2 Amp apparently overheats the voltage regulator, causing it to protect itself by reducing its output voltage and current.