The permanence of a Gothic language in Crimea is a rather problematic question : until recently, the only extensive source about it was Oghier de Busbecq's accounts in his Turkish Letters for a Germanic-speaking people living in southern Crimea. At no point he affirms they were Goth, only to say he couldn't tell if they were Goths or Saxons. He nevertheless made a point to list a series of words from one of two, or both peoples, from the region : a native Germanic-speaker having lost much of his native language, and a Greek having learnt enough of it.

It happens that this part of Crimea, the former principality of Teodoro/Mangup, was also called Gothia by Byzantines : it is not just a late medieval reminiscence of Late Ancient Goths (although, Goths mentions are more probably artefacts in several case) as the Tale of Igor's Campaign does mention "Gothic maids" in the XIIth; and the "Gothic lords" mentioned in the letter of Zachariah, Prince of Matrega, to the Protectors of the Bank of St. George.Mention of Goths in ecclesiastical titles until the XVIIIth century, however, doesn't imply an ethnic or linguistic survival no more than Gothia (roughly lower Languedoc and Catalonia) and Goths being accounted for in the VIIIth to XIth centuries in southern France did.It doesn't implies, however, that these Goths kept a distinct ethnic and linguistic identity, no more than early-medieval Gothia (roughly fitting Lower Languedoc, then Catalonia) and its nobles calling themselves Goths until the XIth century.

So, looking at Busbecq's list, can these words be tied to what we know of Gothic language, trough Ulfila's Bible and other, limited and scattered, sources from the Vth century?It's hard to tell : while there's some phonological elements that makes Crimean Germanic speech relatively close to Ulfila's Gothic language, a lot of phonological and lexical elements seems closer to evolution that happened separately in Low German dialects. While this language might have been called Gothic, it might not have been a direct evolution from Late Ancient Gothic.

We do have medieval accounts, however, with William De Rebruck and John Galafontibus. It doesn't tells much however.

There are great bluffs or capes in this sea from Khersona up to the mouths of Don, and forty or so castles between Khersona and Soldaia whom each have its own language; there is also many Goths, that still use German as their languagez

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Along and around the Black Sea live two small nations: Tats and some Goths. In their religion, they follow the Greeks and use Greek letters. [...] Goths can claim to be descended from the Scots and speak like the English.. They live along the shore near Kaffa, and also in Tartary and Cumania.

But there was certainly a Gothic-speaking population remaining in Crimea, at least until the Xth/XIth century : in 2015, evidence of Ulfila's Gothic language in this sense was discovered on Mangup's basilica as five graffiti. So the question is less if Late Ancient Gothic existed in Crimea, but how long did it survived and why this Germanic speech in late medieval Crimea, while having Ulfila's Gothic elements, tends to look a lot as Low German?

The traditional opposition is about a distinct Gothic language from Ulfila's Gothic having more or less survived as a scattered idiom even in Crimea, and a medieval western Germanic emerging as German speakers (or Anglo-Saxons if you're following the accounts on Nova Anglia on the Black Sea) settling and being influenced by a remaining Gothic speaking population.So far, there's not enough evidence to have a clear and definitive answer, although the regular comparison to western German speeches shouldn't be dismissed.

Regardless of its nature, it survived until the XVIIIth from the reading of Johann Christoph Adelung. He basically say that in place where Goths were believed to have lived, some Tatars (originally Christians) speaks a language close to Low German that he was able to understand sometimes.
Considering it means Gothic language, as a direct descendent of Late Ancient Gothic, survived until the XVIIIth is quite optimistic,to say the least, and not an established fact.

What do we have then?

- Late Ancient Gothic-speakers were still present in Crimea until the Xth century

- People identifying themselves and being identified as Goths lived in Crimea at least until the XVIth century, but their language isn't obviously tied to Late Ancient Gothic, explainable either due to a separate evolution, either due to a Low German influence or dominance with Gothic as a substrate.

- This Germanic language probably living on until the XVIIIth century.