I agree the siren could "help" the attacked ground positions or troops being more alert.
Also i agree the siren could have begin losing its psychological effect as the war progressed.
However, i do not think 1942-43 made a period of high losees of Stukas, at all. 2 remarkable battles in such period in the ostfront can be of help in the issue:
(i) Stalingrad (second half of 1942), losses of fighters, bombers and stukas over and around the city in the Volga were low for the Luftwaffe, being moderate in the worst case scenario.
The brunt of the disaster suffered by the Luftwaffe in Stalingrad, was suffered by the transport branch, losing more than 500 transports and a number of bombers pressed into service as transports during the airlift.
(ii) The Kuban air battles of 1943 where the Stuka flew many many missions in very large formations. Perhaps it was the last place where the Stuka flew in massive formations in world war II.
It was either april or may of that year, in that area, that a 460 Stuka strong formation attacked soviet positions in the western tip of the German bridgehead, losing only 6 Stukas, to soviet AA mostly.
(BTW, a casualy rate far lower than the one the USAAF`s heavy bombers were accepting in western europe).
Early 1943, saw the Stukas gutting US military convoys and grund positions in North Africa, in an environment where the USA did not have air superiority.
(BTW, to those who claim and claim over and over again the Stuka was "obsolete" by even 1942, you should read a bit more on the experiences of the US soldiers being pounded by the Stuka in North Africa)
Does anyone know if the Stukas which pounded the US army in North Africa were fitted with the sirens?