The circuit below is clipped from the datasheet of AD603.
Assume the output of A2 is a dc signal. When the voltage of node 1(see the picture) is changed, say, to 3V, the voltage of node 2 becomes less than 5V, which indicates that voltage cannot stay stable.
I am wondering does it matter? Is it necessary to guarantee a stable voltage at node 2?
You have to do an AGC loop gain (and phase) analysis to check for stability.
Instabilities appear if the loop gain is much greater than 1 and if there are phase changes. High phase changes generally appear at minimum gain (high input power).
This won't ever happen in normal operation. AGC reduces the output voltage swing to about 1.5 Vpp, bias point is 5V. Also the amplifiers are AC coupled, so no permanent DC output voltage can exist.