Usually, the AMR is defined as the point where the performance of the transistor degrades by a certain amount, e.g. the leakage increases beyond a certain amount, or the threshold changes by so much amount.
What this also means is that there will likely be some performance degradation even before you reach AMR. At AMR, you simply cross a certain threshold. So there is some measure of arbitrariness in this definition, as in every definition of parameter limits.

The design manual usually specifies in quite some detail as to how the measurement was done, and how AMR is defined. You should check this out.

In some cases, the AMR may really be defined as the point at which the device suffers catastrophic breakdown although I doubt if many foundries define AMR on this basis. In this case, you would of course be seeing substantial performance degradation way before onset of breakdown, i.e. way before you reach AMR.

Vivek