Decline of the Emperor's power was a gradual process, but was there some decisive point when it was generally recognized that Northern Italy was no longer part of the empire? Were there any negotiations or treaties? Or did the Italian states continue to pay lip service to the emperor until the dissolution of the Empire?
And what about the Netherlands? Before the Dutch rebellion, it was mostly part of the empire, but the wasn't the rebellion against the Spanish crown, not the HRE? Or is it considered to be basically the same thing as both Philip II and Ferdinand I were Hapsburgs?
I hope this question is not against the rule that forbids asking about basic facts, as there is more to it than just a date. If it is against the rules, I apologize.
The OP is accurate when he says that the HRE gradually lost control over Italy. There was no decisive point when the HRE went from having complete control over Northern Italy to having no control.
The HRE was recreated in 962 AD by Otto the Great, after he conquered the Kingdom of Italy in 961 AD. At this point the Kingdom of Italy was similar to many other Western European kingdoms. There was a very limited bureaucracy, and Kings had a limited control over their country. While other countries in Western Europe centralised over the following centuries the HRE didn't, and the power of the Emperor gradually reduced.
The first reduction of power in Italy was the Constitutio de feudis. Which was decreed by the Emperor Conrad II in 1037 to gain support from the lessor nobility and burghers in Italy to defeat a rebellion by Herbiert the Archbishop of Milan. This document as well as the subsequent Libri feudorum. Mainly dealt with establishing a system of laws in Italy, and gave greater rights to lesser nobleman and established them as having hereditary right to their lands. The constitutio also limited the Emperors ability to tax his subjects in Italy by abolishing the fodrum.
Since the HRE also controlled Germany, the Emperor was unable to be physically present in Italy, this required him to grant more indulgences to his Italian subjects so they would support him as Emperor. Also since the Emperor was unable to regularly visit Italy, due to the Alps making travel between Germany and Italy difficult, Italy gained more autonomy.
Frederick Barbarossa attempted to restore Imperial power in Italy, however the Italian cities who had gotten used to their autonomy formed the Lombard League in 1167 with support from the Pope. After years of fighting Emperor Frederick lost the Battle of Legnano in 1176, which resulted in him signing the Treaty of Venice in 1177 and the Peace of Constance in 1183. The treaty of Venice mainly dealt with recognising Pope Alexander III as the Pope and lifting the excommunication on Frederick I, it also established a 6 year truce. The Peace of Constance granted Italian cities the right to elect their own councils, and enact their own laws. However the cities and their rulers had to swear fealty to the Emperor. While the HRE didn't lose any territory their control over Italy was greatly weakened
The grandson of Frederick I, Frederick II tried to restore Imperial authority in Italy, this led to the formation of the Guelphs (who opposed him) and Ghibellines (who supported him). With the death of Frederick II in 1250, and his son Conrad IV in 1254, the Emperor lost control over the Ghibellines who eventually become their own faction which was mostly independent of the Emperor.
The HRE never regained control over Italy, the Habsburgs who were Emperors from the 15th century onwards, also held various other titles, such as the King of Naples through the use of these titles they exercised some control over Italy, however since the reason the Habsburgs gained power in Italy wasn't due to them being the Emperor this shouldn't be seen as a restoration of imperial power in Italy. Especially considering the fact that in 1558 Habsburg territories were split between the Austrian and the Spanish branches, and the Italian territories remained with the Spanish branch, whereas the title of HRE went to the Austrian branch.
Imperial control over Italy officially came to an end in 1797 with the Treaty of Campo Formio between France and Austria, where the Holy Roman Emperor Francis II was forced to renounce all claims to the Kingdom of Italy. Although Austria continued to hold some territory in Italy.
As for the Netherlands there was originally no political entity known as the Netherlands, instead there were various different counties who each controlled a part of the Netherlands. All of these counts were vassals to the HRE. These counties and some others eventually merged in a personal union under the House of Burgundy, which was a cadet branch of the French Royal family.
Due to Charles the Bold, who was the Duke of Burgundy having no sons his Duchy was inherited by his daughter Mary of Burgundy in 1477. Mary was married to Maximillian I who was a Habsburg, who was the son of Frederick III, who was the Archduke of Austria and the Holy Roman Emperor. After Mary died her son Philip the Handsome inherited Burgundy. Philip married Joanna of Castille, who was the Queen of Spain. Their son Charles V eventually inherited all of his parents and grandparents titles.
Due to the holders of fiefs having more power over their territory than the Emperor did, holding the various counties that that made up the Netherlands granted the Habsburgs much more control over the Netherlands than they had while they were Emperors.
When the Habsburg territories were split in 1558 the Netherlands went to the Spanish branch, however the Spanish Netherlands continued to be a part of the HRE, and in their role as the Count of Flanders, Namur, etc. The Spanish Habsburgs were vassals to the HRE. Although Spain itself wasn't a vassal. Therefore when the Dutch revolt happened they were not technically rebelling against the Spanish crown. Just against Phillip II who also happened to be King of Spain.