I never hear of this, so i'm presuming that after Rollo was made Duke, they pretty quickly 'became French', turning away from Paganism and embracing the French systems of feudalism, warfare etc. Was there much in the way of bonds in the latter years, migration from Norway, trade, hiring mercenaries and so on, or had they pretty much turned their back on their Nordic roots?
It is important to distinguish the identical consciousness of shared 'Norse-ness' from the real political-economic-cultural relationships between the Normans in Normandy and their supposed homeland.
As for the latter, 'real' connection, recent Anglo-Phone as well as French researchers come to agreement that the period between ca. 1010 and ca. 1030 should be regarded as a final turning point of disapora Normandy's Normans rupture from Scandinavian World. In other words, Norsemen (including what we call 'the Vikings') more often visited Normandy around 1000 than generally assumed. The Danish fleet sometimes took shelter in Normandy's harbors, and King of England once try to assault the Normans in Normandy for the Norman's favor to their Danish brethens (but failed). The famous marriage between King Aethelred II of England and Emma from the ducal family of Normandy in 1002 should be understand within this political triagles among the British Isles, Normandy, and the incoming Norsemen (mainly Danes): King Aethelred tried to break this kind of 'Viking Diaspora' alliance forged between Normandy and Denmark.
About the same time, some British people still seemingly kept taken in Normandy and seeming kept sold in the slave market in Rouen. The wife of Moriuht, the decadant protagonist of the namesake poem was said to be one of such unfortunate kidnapped victims. The torned couple could finally met again Rouen after some kind of Decameron-esque adventures of the husband (harassed by the Vikings, found shelter in the nunnery and having relationship with almost all the nuns there.....), and Moriuht got famous there as a self-claimed intellectuals. According to this poem, the emerging Franco-Latin Christian atmosphere and the Norse culture still stayed side by side in Rouen around the end of the first millenium.
On the other hand, the supposed 'Scandinavian' origin of ducal family had played a siginificant role in Norman and Anglo-Norman historical writing in Normandy from the turn of the first millenium to the twelfth century. The Normans regarded their origin as a source of their military strength as well as their relative independence against shadowy kings of France. It is worth noting that the Norsemen also showed keen interest in this supposed 'cousins' activity and linage in their emerging historical writings during the 12th and 13th century. [Added]: To give an example, the linage of Count Rollo of Rouen, founder of the Norman ducal family was later identified by them to be a son of Earl (jarl) Rognvald of Møre (Western Norway), legendary founder of the Earldom of Orkney, the northern isles of the British Isles in the saga of the Earls of Orkney (Orkneyinga Saga, Chap. 4), written in the first half of the 13th century. This tradition should be regarded as retrofit, though: We don't know almost anything certain of this Rollo in his lifetime except for a few charters (the translations are found in [van Houts (trans.) 2000]). The earliest witness of such historical tradition is the Historiy of Norway (Historia Norwegie), customarily dated the middle of the 12th century, and it merely states that Rollo (Rodulfus in Latin original) was one of the leaders of the raiding bands, kinda 'organized' by Earl Rognvald (A History of Norway, trans. D. Kunin, pp. 8-9). The later Icelanders even produced a namesake of Count Rollo, Hrolf the Walker (gönga-Hrólfr) and the 'legendary' saga whose protagonist was this namesake Hrolf (not Count Rollo himself). So, Norsemen, the people of Normans' alleged homeland also eagerly tried to incorporate famous Rollo as one of 'their' legendary Viking heroes in the past (probably to boost the fame of the entire latter group further). The most of Rollo's fame as well as his 'Norse' root has been indeed developed as such post mortem historical traditions. So to speak, they were strongly attached each other in their imaginary-literary worlds, despite of their 'real' waning contact.
[Added also]: I don't want to deny the trace of any actual 'Norse' cultural trait altogether from Normans in Normandy from the late 11th century onwards, though. To give a famous example, they did not forget some nautical (ship) technology not entirely. Some coastal place names of Normandy like reefs are said to come from Norse language, and the images of shipa and shipbuilders, depicted in Bayeux Tapestry, testimony of Duke William's conquest of England, are indispensable graphical sources also for the ship-building technology of the Vikings. This tapestry was in fact almost only contemporary source that explicitely show that the viking ship (probably) had famous dragon-head decorations!
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[Added]: Typo fixes, expands in the later half, adds some references.