I know at the very beginning there was some debate amongst the British regarding how much to act on the first decrypted messages regarding shipping traffic, for fear of giving the game away immediately.
Surely as the war went on, even if this reticence by the Allies continued (did it?) Germany would become aware that something was up - did this happen while they still had the resources to develop new cipher machines?
How did this affect dealings with Japan and the other Axis forces - were they ever suspicious or wary of German signalling?
Some of this is addressed in Hugh Sebag-Montefiore's Enigma: The Battle for the Code, my copy of which is not immediately to hand. Although British, it manages to avoid the Bletchley fanboi aspects of a lot of recent writing and concentrates on what is euphemistically called "practical cryptanalysis"; mostly "pinches" of key material. It looks at the way in which the German intelligence viewed the main threat as being some source of key material (they were obsessed with spies and traitors) and never seriously considered that the resources were being put into breaking it cryptanalytically. Therefore they were looking for evidence -- which they would never find -- that the British were reading Enigma material contemporaneously and continually, when in reality there were considerable gaps.
However, the best survey of the issue is Ratcliff 1999 for which you will need a university login or similar for access. Wikipedia has a near-paraphrase of it in the B-Dienst article.
The summary would be that the Germans never mounted a large, well-organised attack on enemy crypto; like a lot of the German war effort, it was silo'd and subject to immense inter-service rivalry and political interference. They assumed that the British wouldn't either. Additionally, they had never noticed the Enigma system's fundamental flaw, of the non-clashing property (A encodes to B through to Z, but never to A), which was the main way in which Enigma was broken subsequent to the changes to the indicator system which rendered the Polish approaches useless. The non-clashing property allowed the range of conjectured plaintexts to be narrowed down, and then allowed the "contradictions" which drove the Turing-designed diagonal board to function. They were convinced that it was secure, so in any situation where Occam's Razor would have said "our crypto has been compromised" they would either ignore it, or would start a wild goose chase for leaks of keymaterial.
All of the German discussions of Enigma's security, whether by
cryptologists or commanders, emphasize Enigma's strength in the face of
statistical attacks. Those who recognized that Enigma could theoretically
be cracked believed serious compromise would require testing virtually all
of Enigma's 3xlO combinations each time the setting was changed, a
process too time-consuming for the conditions of war.
The German military believed that no one could read Enigma currently
(in time to be useful) without both a captured machine and the current cipher settings. Some experts believed Enigma so difficult that the enemy would be lost without the very message settings chosen by the operator at the beginning of each signal."
R. A. Ratcliff (1999) Searching for security: The German investigations into enigma's security, Intelligence and National Security, 14:1, 146-167, DOI: 10.1080/02684529908432527