To be fair, I'd never even noticed the /t/ and /d/ were pronounced there—I had always thought they were simply reduced like many other inconvenient consonant clusters, say, the reduced /t/ in between two /n/s in "I don't know"—that is until I heard it a few days ago when talking to a native speaker who has a particularly clear accent, pretty much model-like. I realized that maybe it's just so subtle that my untrained ears simply can't catch it.
There are many variations in the pronunciation of 'don't know'. The differences are so subtle that many of them can be detected only by a trained phonetician. Some of the more obvious variations are:
1. /aɪdnəʊ/ - The /d/ may not be heard, but it's there. The tongue stops on the /d/ and /n/ part of the alveolar ridge marginally longer than it would if the /d/ were not there. The release of the tongue is for the /n/, not for the /d/. It is context, intonation, facial expression and body language that tell us that this is 'I don't know' rather than 'I'd know'
This version might be considered sub-standard by some people.
2. /aɪdənəʊ/ - the /d/ is clearly released. but there is no trace of the /t/.
3. /aɪdʌnəʊ/ - this is simply a variant of #2, as is #4
4. /aɪdə)nəʊ/ - Of the three (2, 3 and 4), this is probably the one I use in informal conversation
These three are common in informal conversation, though some people claim they don't say them They believe that they pronounce the /t/.
5. /aɪdəʊn(t)nəʊ/ - Very similar to #4, though the tongue stops slightly longer on the alveolar ridge. it's not released as a /t/, but it's there.
6. /aɪdəʊntnəʊ/ - the (non-released stop of the /t/ is slightly longer again.
6. /aɪdəʊnt nəʊ/ - This is the version many speakers of BrE claim they use, but it's actually not very common in normal speech. You'll hear it normally only from people who are deliberately speaking carefully (as in a speech/lecture or an interview), or who are emphasising the negation. The /t/ may be aspirated.
(Note. I have given only a phonemic transcription. A narrow phonetic transcription would make the differences clearer visually, but would not be representative of a wide range of native speakers. it would also require a number of symbols and diacritics that are unfamiliar to non-specialists.)