V can be lost when it acts as a perfect "suffix" (not found in the present stem)
Cser 2016 gives the rule that -v- cannot be lost when it is "part of the lexical makeup of the verb" ("Aspects of the Phonology and Morphology of Classical Latin", p. 117), agreeing with TKR's suggestion in the comments. In other words, -v- usually isn't lost when it is found in the present stem as well as in the perfect stem of the word, which means that lavisti and adiuvisti would not be expected to have v-less variant forms.
Likewise, cavi and favi from caveo and faveo do not show V-less contracted forms (Lindsay, "A Short Historical Latin Grammar", 1915, page 194).
When -v- appears as a "suffix"1 marking the perfect stem, it might or might not be able to be deleted: this isn't completely predictable based on the form, it also seems to depend on the lexical identity of the verb. Cser says that cerno has v-less variants alongside the forms built on crēv-, but sperno has only sprēv- perfect forms.
V-deletion is possible not only for some verbs with -ēvī/-īvī/-āvī perfects, but also for some verbs with -ōvī perfects; Cser gives the example of nōsco with the forms nōvērunt~nōrunt and nōvisse~nōsse.
As Cerberus's answer implies, we don't generally see syncope/syllabic contraction of -ui-/-ue- in the perfect (as in metuisti or metuerent from metuo); based on that, I didn't expect to find forms with contraction for adjuvo. However, surprisingly, Lewis and Short says that some contracted forms are actually attested for this verb:
adjŭro or adjuero = adjuvero, Enn. ap. Cic. Sen. 1, 1: adjuerit = adjuverit, Ter. Phorm. 537
By the way, spelling variation between -uv- and -u- before a vowel is not only found in the perfect, but also occasionally in other contexts. It's unclear to what extent a contrast between /uw/ and /u/ was actually possible in Latin; it has been observed that the spelling -uv- in Latin (that is, syllabic V followed by non-syllabic V) appears almost exclusively in contexts where the use of a single letter V would create a spelling with ambiguous pronunciation (namely, a. when followed by syllabic I and a vowel, where the spelling VI+vowel could be misread as /ujj/+vowel; b. when word-initial, where the spelling V+vowel could be misread as /w/, c. when preceded by consonantal I, where the spelling IV could be misread as /iw/) ("The cycle without containment: Latin perfect stems", by Donca Steriade, 2012, page 62).
Violations of this rule apparently exist, but seem fairly marginal
The rule that Cser gives is sometimes violated for verbs with -ōvī perfects: moveo, mōvī and apparently also voveō, vōvī can lose the v at the end of the perfect stem, even though v is also found at the end of the present stems of these verbs. The v-less forms of these perfect stems don't seem to be common, though. Cser says that
For nōv- with -is-class affixes, the ratio of deleted forms in the corpus I used is 96.3%, for mōv-
(including prefixed forms) only 3.6%.
I found mention of contracted forms of the perfect stem of voveo (specifically, dēvōrō for dēvōverō in the future perfect) in the first page of "Philological Notes" in The Classical Review, Volume 3, Issue 6 June 1889 , pp. 243-246, by Fred. W. Walker. Unfortunately, I can't access any more pages there. I would assume that the specific forms given there are accurate, but I'm not sure how accurate the article as a whole is, given that it seems to argue that amavisti had a long vowel in the penultimate syllable and that the short forms of the perfect were older than the long forms, neither of which I think has become a mainstream position.
- I put "suffix" in quotation marks just because the morphological structure of Latin perfect forms can be analyzed in different ways, and it's not always easy to divide a perfect form into parts.