I saw a great number of Latin inscriptions in a cathedral on Malta, dating roughly between 1500 and 1800 CE. There were at least a couple of instances of the word monimentum, but saw no monumentum. Is the spelling with I instead of U common in the Latin of that era? I do not recall seeing it before, and I am under the impression that it is classically exclusively monumentum.
Since your question is about the use of i-u in Post-Classical Latin, I will address that point only and not its use in Old or Classical Latin.
I don't have enough information - yet - about the specified time period and place (1500-1700, i.e. Neo-Latin in Malta), but here's what I've been able to find about Medieval Latin.
Peter Stotz (Stotz 1996, Handbuch zur lateinischen Sprache des Mittelalters, volume 3, p. 42) writes the following:
"Das Schwanken von i und u for Labialen im röm. Latein äußert sich im MA nur noch in Form vereinzelter Schreibung, welche durch den uneinheitlichen Befund in den damals vorliegenden älteren Texten verursacht sind.
in English: The alternation of i and u before labials [found] in Classical Latin manifests itself in the Middle Ages only in the form of isolated spellings, which is caused by the inconsistent findings in the older texts available at that time.
cf. "Gewisse Schwankungen zwischen ĭ und ŭ in älterer Zeit haben sich durch ihr Vorkommen in den älteren Texten ins MA fortgeschrieben" (p. 69).
Here's the relevant entry from Niermeyer's Mediae Latinitatis Lexicon Minus:
We need to look it up in part 2 of Ijsewijn and Sacré 1998 Companion to Neo-Latin Studies for Neo-Latin data - I don't have a copy at home.
Re: Neo-Latin editorial (spelling) practices, here's what Tom Deneire (Deneire 2014) says:
"Unlike classical texts, for which the original spelling can almost never be ascertained, Neo-Latin texts often exist in authorial copies (either in manuscript or in print) that reflect the author’s particular spelling of the Latin language. This spelling might be based on a consciously adopted system [...] or be completely haphazard [..] . In this way, one may encounter mediaeval remnants (lachryma), forms inspired by the vernacular (ottinere), hypercorrections (caeteri), just typical Neo-Latin spellings (caussa), or as regular a phenomenon as the reversal of u and v that produces spellings like vua (‘grape’)" [emphasis mine - Alex B.].
Considering that this is a word-internal short vowel before a labial consonant, it looks like this vowel comes from the "sonus medius".
Unfortunately, I don't know that much about the patterns of variation in the use of u vs. i in the spelling of words like this. I was able to find the following passage in B. Kennedy's Latin grammar, Fifth Edition (1879):
the middle sound between ĭ and ŭ [...] exists almost exclusively before labials [...] Inscriptions shew that the forms with ŭ prevailed in E. L., and R. L., those with ĭ in and after the Augustan age, for which the Monument of Ancyra, as edited by Mommsen, is the best authority.
(pp. 31-32, §12)
Allen's Vox Latina also says that u variants tend to be older, and i variants more recent: he says "the earliest example for this change is from 117 B.C., with inscr. infimo beside infumum" and "in some cases, although the change took place, the older u form came to be preferred (e.g. documentum)" (p. 57).
Speaking generally, Allen writes that
The change of official orthography from u to i in such words is said to have been due to Caesar (†Varro, cited in Cassiodor(i)us, K. vii, 150; cf. Quintilian, i, 7, 21); and Cicero is said to have considered the older pronunciation and spelling as 'rusticanum' (Velius Longus, K. vii, 49). Velius Longus (67) also mentions that Augustan inscriptions still showed u; but i is in fact regular in the Monumentum Ancyranum.
I wasn't able to find the word monumentum/monimentum anywhere in the text of Res Gestae Divi Augusti, so the Monumentum Ancyranum doesn't seem to provide any evidence about this particular word.
There seem to be a fair number of hits for both monum- and monim- in the PHI Classical Latin Texts database: there were 581 matches for
$monum, but also 123 matches for
#monim, including some from the works of Cato, Plautus, Caesar, Cicero, Ovid, Pliny, and Virgil.
Based on this, it seems to me that monimentum existed in the classical period, and it doesn't seem to have been extremely rare or considered an improper form. I'm not sure how its frequency changed in later time periods.
Robert Ainsworth's Dictionary, MDCCXXVII,lists mŏnĭmentum first with mŏnŭmentum second, and included in only one of the quotations (Cic.).
mŏnĭmentum examples (various meanings) from Horace, Virgil, Cicero, Tacitus, Ovid, Plautus.
This is followed by entries (sharing etymology from moneo) for monitor, monitio, monitus.
mŏnŭmentum gets a shorter entry. It gives doceo as the paradigm for that formation, but points out that derivatives of doceo form docu- (videlicet: dŏcŭmen, dŏcŭmentum,) For meanings and citations it refers back to monimentum. But Ainsworth may be eccentric, or obstinately pedantic in his preference; I don't have access to 16th, 17th, 18th Century editions of Latin authors.
Sir Christopher Wren's tomb in St Paul's Cathedral, 1723, bears the inscription Lector, si monumentum requiris, circumspice.