Do we need isolator after power amplifier in a microwave circuit?
An isolator before the antenna improves the antenna reflection coefficient.
Some amplifiers will have a tighter load reflection specification than others.
If the load sends back a large reflection, this will create a standing wave with the out-going signal. A 100% reflection will double the voltage in some places, and double the current in others, above what the amplifier would normally see when driving a properly matched load.
You need to study the data sheet for your particular amplifier, to see what the maximum permitted output power is for any given load reflection coefficient.
Different amplifier technologies will have different limiting parameters, and different amounts of standoff between operating and damage levels. Why should a TWTA be more fragile than a solid state amplifier? Let me wildly speculate that the semiconductors in a SS amplifier are fairly poorly controlled, so are operated conservatively. Conversely, the vacuum tube can be manufactured very accurately, and so can be operated very close to breakdown with confidence, leaving little margin for peaks in voltage due to reverse power. Alternatively the SS amplifier is lower impedance internally, so could be current/thermal rather than voltage limited? Speculation over. Comments welcomed from people who know what they're talking about on the details of amplifier VSWR overload.