Two important questions. What type of transistors are in the amp and what type or model power supply do you have? Chances are that old amp runs something like a pair of MRF455's and I can't see this drawing more then 20 amps. Your power supply should be capable of running that amp especially since it is the only load on the supply and it's intermittent.
What is happening is that you are triggering the current limit protection on the power supply. The positive peaks of your audio are briefly causing the current to rise just above the point where this protection is set. If the supply has more then one potentiometer inside, one of them is most likely the voltage adjustment and the second is the current limit.
You can make this amp work with you power supply one of two ways. You can turn the voltage down so it draws less current but if it uses pass transistors, they may get hotter. You could also set the current limit just high enough so it runs the amp while checking the voltage. If it can't hold the voltage under load, you should set that lower. Don't get long winded and check the power supply to make sure it's not over heating.
Another thought I just had is you don't mention if this 80 watts on low is PEP with audio or if your meter is measuring average power. You may be overdriving the amp on high power. If the supply shuts down on high power without audio on AM, this is a sure sign the carrier is too high. I would only run this equipment together if the carrier were set at or below 40 watts assuming the 160 is a PEP rating.
