Pronunciation of 'damning' with /n/
Solution 1:
The n in words like damn, condemn, solemn, autumn is silent because the cluster /-mn/ violates the Phonotactic rules of English. Phonotactic rules are language-specific rules that determine the permissible sound sequences in a particular language. According to English Phonotactics, 'two nasals cannot occur next to each other within the same syllable'. Donka Minkova says 'the cluster [-mn] is perceptually opaque because of the overlapping features of the two adjacent nasals'. [A Historical Phonology of English]
According to A History of Modern English Sounds and Morphology by Eilert Ekwall, the loss of n after m is attested from the 16th century. Eilert goes on to say that the [n] was lost regularly in final position and before consonant (e.g. solemnly). Dobson says that the loss of [n] can be attributed to the loss of final e ([ə]).
Almost all these words that end with -mn came from French and had a final [ə] after the -mn-, so the [n] must have been pronounced because there was a vowel after the -mn- which would split up the cluster /mn/.
In some cases, the /n/ gets pronounced when a vowel-initial suffix (such as *-able, -ation, or -er) follows the ‹mn›, where the [n] is resyllabified as the onset of the next syllable, though the pattern is very irregular. Damnable is pronounced [ˈdæm.nəbl̩] — the vowel in ‑able splits up the cluster /mn/. The same thing happens in damnation, solemnity, autumnal, condemnation, hymnal etc (I.e. the /n/ is resyllabified as the onset of the next syllable).
The /n/ doesn't get surface in inflectional words such as damning, damned, hymning, hymned, condemning, condemned etc. Eilert says that they're influenced by damn, hymn, condemn.
Damning is not pronounced with an /n/ in Modern English. William Henry in How Should I Pronounce? Or, The Principles of the Art of Correct Pronunciation says that 'damning' is not pronounced with an /n/:
However, some sources claim that the pronunciation with an /n/ has existed. A Practical Dictionary of the English Language by Noah Webster does list the pronunciation with /n/:
John Walker in his Critical Pronouncing Dictionary also lists a second disyllabic pronunciation for damned, where the /n/ gets pronounced:
Also from Fowler's Modern English Usage (p195):
damn. In all uses as n., adj., v., and adv. the n is silent; also in the oblique forms damned (but often disyllabic in verse), damning. The n is sounded in damnable, damnation, damnatory, damnification, and damnify.
About limn, Fowler says (p461):
... the base-form is, like solemn, pronounced with the n silent. The inflected forms are limns /lɪmz/, limned /lɪmd/, limner /ˈlɪmnə/ and limning /ˈlɪmɪŋ/ or /ˈlɪmnɪŋ/.
The -ed endings were pronounced with a separate syllable back in Middle English, so banned would've been pronounced with two syllables. In Early Modern English, however, the unstressed vowel in the suffix -ed was lost (except after /t/ and /d/). So after a voiced sound, the -ed became /d/ and after voiceless sounds, it became /t/.
In most adjectives such as wicked, naked, blessed, crooked etc., the vowel remained, so the -ed is still pronounced as a separate syllable in those words. I assume damned followed the same sequence at some point, that's why John Walker lists the disyllabic pronunciation. In Modern English, however, both damning (v & adj) and damned (v & adj) are pronounced without the /n/. Or the adjectives lost their /n/'s due to analogy with damn which had no /n/.
From Modern English Grammar on Historical Principles (7 vols.). 1–7 (1949) by Otto Jespersen.
Loss of final /n/
After /m/, a final /n/ has been lost (assimilated to /m/): damn /damn/ now [dæm], condemn, hymn, limn, column, solemn, autumn. The loss is shown by such inverse spellings as solembe, (Sh LL V. 2.118, quarto of 1598); C 1627 expressly says that n is mute in solemne and hymne. N has been everywhere retained in spelling, except in occasional dam (for damned?: Meredith EH 134 “and dam rum chaps they were!”).
Homonyms: damn = dam, hymn = him, limn = limb formerly lim.
Before a vowel, /n/ is retained: damnation, condemnation, damnable, autumnal, solemnity. Before ‑ing /n/ was formerly heard in “the solemn articulation of damning, condemning etc.” (E 1766, also Walker); now the pronunciation without [n] has been analogously extended to these forms, though the NED has both pronunciations for the participle (but not the verbal noun) damning and recognizes [ˈdæmnɪd] as a poetical form of damned by the side of [dæmd].
I think the shift from amn’t to ain’t is also relevant. The contraction of am not used to be amn’t, where we see the same cluster /mn/, but it got reduced to /n/. Here it’s /n/ and not /m/ because of the following /t/, and also per Phonotactics because:
a nasal following an obstruent in the coda should be homorganic (having the same place of articulation) with the obstruent.