This is one gets into reading tea leaves a little bit.

The distinct (not unique) problem that dealing with Greek culture in Bactria (and indeed western Central Asia as a whole) is there's an almost complete lack of contextual literary sources, and no regionally authored ones, whether by Greeks or any nearby peoples. All accounts of Bactria, and Greeks in Bactria specifically, that we can read as a piece of prose are from far outside the region and, in many cases, from a later period. Much of the region's history has had to be reconstructed from archaeology, and indeed until the 1960s mostly from numismatics, i.e coins. Entire reconstructed histories of the Greco-Bactrian state were written purely on the basis of what could be suggested or reconstructed from coinage until full archaeological sites were unearthed and examined.

That also means that attempting to understand when anyone identifying as 'Hellene' finally vanished from Bactria, and western Central Asia more generally, also has to be done archaeologically, which has fundamental weaknesses. The biggest of those is that objects are not automatically representive of somebody's descent. In other words, objects with Greek design influence do not automatically mean the person who made it or used it was Greek, and vice versa. You can make some assumptions based on diagnostic pieces of material culture but only really about cultural identity, and Bactria as a region is generally demonstrative of cultural boundaries being eroded, rather than reinforced, particularly the later in time one gets.

There has also been a suggestion that the famous Gandharan Greco-Roman influenced material culture was not itself representative of a surviving, distinct Greek culture within western Central Asia (Gandhara basically being the other side of the Khyber pass from Bactria) but instead represented a specific, new infusion of Greco-Roman art into the region as a result of the massive cultural and economic influence of the Roman Empire well outside its borders, possibly to the point of exporting craftsmen. That, of course, is not itself proof that there was nobody in Bactria, or nearby regions, who still identified as Hellenes and represented a continuity of cultural identity with the Hellenistic period, but it is a suggestion that further erodes the notion that material culture exists in a 1:1 ratio with a people's descent.

So where does that leave us with your question.

Even separate to the problems of using material culture to identify the presence of a specific cultural identity, the distinct elements of Hellenistic Greek culture that so strongly influenced the wider region around Bactria also start to blend into a general style that then no longer specifically suggests Greek heritage through its presence. What to us are identifiably Greek influenced styles in statuary, coinage, architecture et al start to become simply a part of general regional culture and no longer even pretend to suggest anything about who is making the object. Attempting to use that process to try to identify a period in which specifically produced 'Greek' cultural items lose their specific significance and simply become adapted into a vernacular style stretching from Central Asia to the Indus region is, as you'd imagine, difficult for the reasons we've just got into about how material culture doesn't automatically signify personal identity, particularly in a region with multiple cultural influences all of whom, by the 1st century AD, had already started to blend together.

This is where the lack of any literary, narrative context for this period really starts to hurt.

In terms of Greeks in India the last Indo-Greek statelet seems to have been occupied by the Kushans (whose heartland was Bactria) in the 1st century AD. That by itself doesn't automatically suggest that Greek cultural identity was still a living heritage in Bactria, but the Greek communities in these regions were closely connected to one another, at times directly and politically. It provides at least some semblance of a cutoff date for this question. But I've never seen a work actually figure out any sort of real rubrick for pinning down to a real date.

Purely going by what other scholars have suggested, different estimates of date ranges have been between the 3rd-5th centuries AD for the full disappearance of any distinct regional Greek identity in this part of the world. But the reason I didn't just open with that is, given all of the context I've just added, you can see why it's very hard to actually feel secure even about a rough date range. It's why it's like reading tea leaves a bit. The genuine and honest answer is that we simply don't know to any degree of certainty, but that estimates veer on the side of 'Greek cultural identity had vanished from the region before the collapse of the Western Roman Empire'.

As for its longevity, you can potentially boil that down to a few things in my opinion. The fact that Bactria was a heavily urbanised, agrarian region with a history of complex state societies dating back to the Middle Bronze Age, meaning that there were well established state structures to be usurped by whichever group of elites managed to monopolise power there. The fact that, unusually for imperial powers that controlled the ancient Near East, the Seleucids did not control the dynasty's original homeland of Macedonia, and so political power in the nascent Seleucid state was propagated via a deliberate settling of Greeks into urban sites across the empire, including the crucial region of Bactria. The fact that the breakaway of Bactria from the Seleucids was led by a Greek dynasty, in a period in which Greek speakers had monopolised the highest levels of power across the region. The fact that Bactria seems to have been conquered and incorporated into states that preserved many of its original power structures, even though they ultimately probably began to erode them over time in favour of their own, i.e Greeks simply became a quirky local additional elite group in the region in the same way that the remaining Persians in Bactria did the same through being the previous socio-economic elite in some crucial administrative functions. Last but not least, the inertia of the fact that the Greek presence there, whether under Alexander, the Seleucids, or the Greco-Bactrian dynasties, was originally imperial, and during their period of imperial dominance, accrued material and cultural power that came to give them lasting significance even after the end of their dominance in that region.