I recently suggested that the virtual absence of mediofinal "h" in Etruscan is a feature common to both Lemnian and Rhaetic as well but it may not be clear to my readers why I'm insistant on that idea, so let's discuss.
Just to be sure, I looked up in my database what words contain medial h. Of the more than thousand entries I have, I came up with only two results: cehen 'here before' and the name Uhtave. The name Uhtave is clearly of Oscan origin, from Úhtavis, and related to the common Roman name Octāvius. It is squarely an Italic, and hence, un-Etruscan name. The word cehen, while a native word, does not in reality show an archaic medial h afterall because it is transparently a recent compound composed of cei 'here' and *hen 'before' (c.f. hanθe 'in front'). Even if these two lonely items were attributable to a pre-Proto-Etruscan stage though, it would need a clear explanation as to why so few instances of mediofinal h exist in this language.
My attentive readers may have noticed that I've already asserted several times on this blog that -va (a plural inanimate ending) is an allomorph of -χva. The term allomorph is just linguistobabble for a piece of language, such as a suffix, that shows predictable variation in its form in different positions or circumstances. So in this case, we may observe that Etruscan -va always pops up after nouns ending in vowels or in sibilants like s or ś, whereas the Etruscan speakers regularly chose -χva when the preceding noun stem ended in most other consonants. Some may wonder why I'm so sure that they are allomorphs of a single suffix instead of two distinct suffixes, but we can put this skepticism to rest right away.
The evidence for allomorphy in the inanimate plural is clear after examining the pair maχ '5' and muvalχ '50'. Lo and behold, we find the same internal alternation of χ and v and for the same reasons. We know that letter chi is used for the sound /kʰ/ (as in Classical Greek) and the letter vee is used for what is in fact a bilabial approximant /w/ (much like Classical Latin vinum 'wine', also pronounced with initial /w-/). Clearly then there is an original sound, let's label it Q for now, that evolves into both chi and vee in Proto-Etruscan based on environment. Through this sort of internal reconstruction, we may then hypothesize that pre-Proto-Etruscan probably had the following items: *maQ '5', *muQalχ '50', and inanimate plural *-Qva.
All we need to do is figure out what the quality of this original phoneme is and we're home free, right? The answer to the mystery of the paucity of /h/ in mediofinal positions in Etruscan, Lemnian and Rhaetic, quite simply lies in this alternation of chi and vee.
So if we now replace our mystery phoneme *Q with *h, everything is resolved. We can both phonetically explain the origin of the alternation as well as explain the curious disappearance of h in both word-internal and word-final positions. Most likely, medial *-h- which was probably a velar fricative became weakened at some point intervocalically and after sibilants. The only thing that remained was the "backness" of the sound which came to be reinterpreted as /w/ and consistently written with the letter vee once the ancestors of Etruscans, Lemnians and Rhaetic finally adopted their alphabet. In other positions, a velar fricative can easily harden to a velar aspirated stop, hence this would explain the evolution to chi after certain consonants and in word-final position. We may then be so bold as to predict the following for a pre-Proto-Etruscan stage: *mah '5', *muhalχ '50' (probably < *mahálχu), and an inanimate plural marker *-hva.
(May 20 2008) I corrected my confusing flaw that Tropylium has mentioned to me. My hypothesized antecedent form of the Etruscan inanimate plural should be *-Qva (and thus in conclusion *-hva) rather than *-Qa and its result *-ha as I had initially written. Naturally, since this hypothesized *h should only result in either Etruscan chi or vee based on the pair '5' & '50', and since the Etruscan form of this suffix, -(χ)va, usually shows both sounds together, then *-hva would seem to be in order. Although, *-ho might also be a possibility if it can be shown that word-final *-o normally erodes to *-a with residual labialization. Sorry about that. There are a lot of details here.