Pronunciation of ‘monotonous'

The phonetic syllabification corresponding to "monotonous" ("mo.not.on.ous") is /mə 'nɒt ən əs/. This is the "leisurely" pronunciation; in most speech occurrences it would be /mə 'nɒt n əs/. The reason for not having "mono.tonous" as the syllabification is for one that there can be only one single phonetic vowel per phonetic syllable and for two that words of three syllables or more, ending in "ous" not preceded by e or i or more than one consonant* are stressed on the third syllable from the end, bar exceptions (desirous, …).

• can.'tank.er.ous, 'ad.ult but a 'dult er ous, ad.'vent.ur.ous, 'am.our.ous, a.'nal.og.ous, a.'nom.al.ous, a.'non.ym.ous, 'ard.u.ous, a.'ssid.u.ous, a'synch.ron.ous, au.'ton.om.ous, bar.'bar.i.an but 'barb.ar.ous, 'blas.phem.ous, 'carn.i.vore but car.'niv.er.ous, 'cav.ern.ous, 'circ.u.it but cir.'cu.it.ous, 'cred.ul.ous, 'dec.or.ous, 'err.or but e'rron.e.ous, 'fat.u.ous, 'garr.ul.ous, 'gel.a.tine but ge'lat.in.ous, 'glam.or.ous, 'glut.en. and 'glut.in.ous, 'glutton/'glutt.on.ous, im.ˌpet.u.'os.it.y but im.'pet.u.ous, 'in.cest but in.'cest.u.ous, …

The principles of pronunciation cited, except for the third-syllable-from-the-end pattern can be verified in the Longman Pronunciation Dictionary and An Introduction to The Pronunciation of English by A.C. Gimson and Susan Ramsaran. The third syllable rule is deducible from an examination of the dictionary just mentioned.

*A research by user Peter Shor gives the following examples.
disastrous, enormous, momentous, tremendous
We can add "stupendous" and "portentous" but there are at least two exceptions: "ludicrous" and "marvellous".

It's probably because of English stress patterns. English has very complex stress patterns. In most cases, the antepenultimiate syllable (third last syllable) tends to be stressed.

The main stress often moves to the antepenult when the suffix -ous is appended to a word.

Examples:

• Glorious -> /ˈɡlɔː.ri.əs/
• Monotonous -> /məˈnɒt.ən.əs/
• Dangerous -> /ˈdeɪn.dʒ^ər.əs/
• Adventurous -> /ədˈven.tʃər.əs/
• Furious -> /ˈfjʊə.ri.əs/
• Humorous -> /ˈhjuː.mə.rəs/
• Contiguous -> /kənˈtɪɡ.ju.əs/
• Ludicrous -> /ˈluː.dɪ.krəs/

Monotonous follows the same pattern and I don't think it has anything to do with the prefix it's derived from.

Compare monotonic /ˌmɒn.əˈtɒn.ɪk/ -- Words that end with the suffix -ic are often stressed on the penult. So I guess it has to do with English stress patterns.

And when monotonous is stressed on the antepenult, the vowels in the unstressed syllables get laxed as usual. Therefore, it's pronounced /məˈnɒt.ən.əs/.

However, there are some words that have only two syllables, and words that have three syllables but the primary stress moves to the penult (second last syllable) when the suffix -ous is appended:

• Disastrous -> /dɪˈzɑːs.trəs/
• Tremendous -> /trɪˈmen.dəs/
• Stupendous -> /stjuːˈpen.dəs/
• Momentous -> /məˈmen.təs/
• Enormous -> /əˈnɔːr.məs/

There's a fairly regular pattern for these words: if the penultimate syllable is heavy, it’s stressed; if the penultimate syllable is light, the antepenultimate syllable is stressed (it also holds true for most of the words that are stressed on the antepenult i.e. the penultimate syllable is light and the antepenultimate syllable is heavy).

• Light -> short vowel and no coda.
• Heavy -> long vowel or diphthong and/or has a coda.

In the above words, the emboldened syllables are heavy, hence stressed.

There may be loads of exceptions, however.

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Update (August 20, 2020):

Luigi Burzio in his book Principles of English stress (chapter 3) writes:

It has long been known that English lexicon does not exhibit a uniform metrical behaviour, but breaks down into two major subsets, whose rightmost stress conforms to either of (1) or (2).

(1)
a. Heavy penultimate, if there is one:
agénda, appéndix, horí:zon.

b. Otherwise, antepenultimate:
américa, ásterisk

(2)
a. Superheavy final, if there is one:
prevént, decí:de

b. Otherwise, penultimate:
inhábit, imágine

Head over to Principles of English stress for more explanation.