Is high tone retention typologically true? When one of the two adjacent vowels at a word boundary undergoes deletion, one of the two tones also undergoes deletion. And it is said that high tone is always retained regardless of whether it was originally associate with the surviving or with the deleted vowel. Are there any examples?
This is a pretty complex topic. The standard theoretical account is that a vowel deletes, its tone is not deleted, and then it associates with "the other vowel". This gives you the Lomongo pattern, where (1) the language has H, L, Rise and Fall at the word level and (2) syllable fusion results in even more conplex tones. In this language H#L→Fall and L#H→Rise (Fall#H→Fallrise...). Under the premise that Fall is the combination of H+L on one unit, the generalization is that all tone are preserved under vowel deletion (and realized on the surviving vowel). So you do not always delete a tone.
When we speak of "H tone retention", we mean something less general, i.e. whene a tone is deleted: retention of H and only H, not other tones. An example of that type is in Kerewe, where /ba-ka-óléka/→ [bakóóléka] 'they showed': the combination L + H is realized as H. It is important to know that Kerewe has no rising or falling tones. In other words, the tone retained has a connection to the kinds of contour tones allowed in the language. One concrete account of the Kerewe-type pattern is that there is a representational asymmetry: only H tones are specified, apparently L tones are actually phonologically toneless. This automatically gives you "H tone retention", since there is no L to retain. An alternative is to specify both H and L, and have rules that delete L when both H and L associate with a single vowel. Or, if the language has fall but not rise, deletes L before H on a single vowel.
To the best of my knowledge, no language has "L tone retention" in the sense of having H and L, and always preserving L at the expense of H under vowel deletion. There are a few thousand tone languages, so I may have missed an example, but "L tone retention" is either extremely rare or nonexistent. There are cases which are not actually L retention, such as the common pattern in Luhya languages where L+H→H, but in case a H follow, i.e. you have L+H+H, the result is L+L+H. For example Logoori /kʊ-éyáa/→[kweeyáa] "we are sweeping", vs. /kʊ-érema/→[kwéérema] "to float". This is explained if tone is preserved in the usual fashion, but then other rules modify the resulting contour tones (Logoori has falling but not rising tones). Accordingly, the result of syllable merger would be kweérema, kweéyáa, then H which is part of a rising tone deletes before H, finally, remaining rising tones become H.
To keep this from getting any more complex, I will just mention that this pattern is not just about vowel deletion, it also shows up in systems of melodic tone mapping, such as Shona which has inflectional tone that mark certain tenses, and where there is a "preference" to preserve the Hs at the expense of the Ls in this mapping.
So I take "H retention" to refer to retention of H at the expense of some other tone (typically L), given a case of two tones where only one is possible (following whatever the rules there are in the language). Some combination of underspecification and phonotactic deletions will give the H retention pattern: there are quite a number of such cases. "L retention" would be retention of L at the expense of H, and that pattern may not exist at all.
Also as far as I know, patterns of tone retention under syllable merger are not divorced from general phonological patterns (they are not a quirk about keeping a tone that is set afloat). Theoretically, one could have a parameter like "when syllables fuse, keep the H tone" which is independent of output that simple reassociation of the Lomongo type would give. Instead, tonal output can be reduced to saying e.g. "Fall (Rise) does not exist in this language", plus the core "H retention generalization" which is that Fall and Rise become H under context-free contour simplification.