This issue comes up from time to time, so let me add a little information so you understand what is happenig, why it's happening and why the protection is important as well as ways to circumvent problems whenever possible.
Low line voltage is typically caused by too much resistance (actually impedance) in the conductors feeding the power source that the amp is plugged into. The voltage drops as the load (current draw) increases. The two most common causes of this are the power source's wires being too small for the load and the distance of the power cable (including inside the walls and extension cords) causing the voltage drop.
In the "good 'ol days", amps were not terribly powerful, efficient, or high performance. They were also not terribly reliable, so while low supply voltage certainly caused performance reduction the impact on reliability was not as easily seen because amps failing was pretty common. As power amps became bigger, more sophisticated, higher performance, reliability had to increase otherewise the cost of ownership was be a deal killer for this better technology. As general reliability increased, the failures due to low line voltage became more obvious. Protection circuits were developed to prevent the damage due to such problems and were infinately better than a failed amp and costly repair.
Currently, with switchmode power supplies and class D amplifiers, the performance bar has been raised again and it because of the nature of the new topology additional attention has been put towards improving the reliability even more. In quality SMPS/class D products (especially the pro level PA amps and bass amps), a lot of thought has gone into studying all of these failure mechanisms and by properly designing around and protecting against these (including low line voltage), reliability has been improved significantly which is why you are seeing longer, transferrable warranties as an end user. It's up to the designer to choose a design that protects against damage but is not unnecessarily sensitive to unimportant conditions. Some companies do a much better job than others.
In general under normal operating conditions, our amps operate down to ~95 to 98 volts, though if there is a lot of power line distortion (looks like a clipped voltage waveform) which can be especially damaging, this threshold will effecively shift up to around 100 volts. In any case, these are pretty severe conditions, not something that I would want to operate any piece of costly elctronics on because of the very real potential for damage.
How can you avoid this problem? The first step is to insure that the wiring (including extension cords) is sufficient for the load and distance. In the USA, with 120 volt mains circuits, either 15 or 20 amp circuits are available. 12 gauge extension cords will minimize the voltage drop due to load, and if the problem persists the only pracical solution is to reduce the load on the circuit. This means either using another available circuit or removing load (such as lighting).
