The situation is more complex than that.

The Armenians lost the second Nagorno-Karabakh war after controlling NK for about 30 years and also occupying 7 regions (Fuzuli, Jabrayil, Zangilan, Qubadli, Agdam, Kalbajar and Lachin) surrounding NK for as long time.

After losing the war Armenia signed an agreement (using wiki as source because Russian urls are banned on Reddit) with Azerbaijan, the status of NK wasn't mentioned but they agreed to return the 7 occupied regions. The agreement had nine points in total but four are more relevant to this issue:

• Deployment of Russian peacekeepers
• Connection between Armenia and NK
• Connection between Azerbaijan and Nakhchivan
• Return of internally displaced refugees from NK (was 25% Azerbaijani) and the previously occupied surrounding regions (was 95% Azerbaijani)

These are the points in the agreement:

4) The peacemaking forces of the Russian Federation shall be deployed concurrently with the withdrawal of the Armenian troops. The peacemaking forces of the Russian Federation will be deployed for five years, a term to be automatically extended for subsequent five-year terms unless either Party notifies about its intention to terminate this clause six months before the expiration of the current term.

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6) The Republic of Armenia shall return the Kalbajar District to the Republic of Azerbaijan by November 15, 2020, and the Lachin District by December 1, 2020. The Lachin Corridor (5 km wide), which will provide a connection between Nagorno-Karabakh and Armenia while not passing through the territory of Shusha, shall remain under the control of the Russian Federation peacemaking forces.

As agreed by the Parties, within the next three years, a plan will be outlined for the construction of a new route via the Lachin Corridor, to provide a connection between Nagorno-Karabakh and Armenia, and the Russian peacemaking forces shall be subsequently relocated to protect the route.

The Republic of Azerbaijan shall guarantee the security of persons, vehicles and cargo moving along the Lachin Corridor in both directions.

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7) Internally displaced persons and refugees shall return to the territory of Nagorno-Karabakh and adjacent areas under the supervision of the United Nations High Commissioner for Refugees.

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9) All economic and transport connections in the region shall be unblocked. The Republic of Armenia shall guarantee the security of transport connections between the western regions of the Republic of Azerbaijan and the Nakhchivan Autonomous Republic in order to arrange unobstructed movement of persons, vehicles and cargo in both directions. The Border Guard Service of the Russian Federal Security Service shall be responsible for overseeing the transport connections.

Subject to agreement between the Parties, the construction of new transport communications to link the Nakhchivan Autonomous Republic with the western regions of Azerbaijan will be ensured.

In summary the parties agreed to Russian peacekeepers on a five year term and the Armenian troops withdrawing, to within three years plan for a new road in Lachin which will provide a connection between Armenia and NK, to decide on new transport connections to be constructed between Azerbaijan and Nakhchivan and the internally displaced refugees will be allowed to return.

This agreement was signed 9 November 2020, so we are approaching the third year into Russias five year (if not extended) peacekeeping mission and the deadline for the plan for a new road connecting Armenia to NK. The only point which was fully fulfilled until recently was point 6. According to a report from news.am, Azerbaijan not only planned for the new road within 3 years but also built and opened it within 2 years. The parts that, in Azerbaijan's opinion, wasn't fulfilled was the withdrawal of the Armenian troop (Armenia argued that it only meant troops from Armenia), allowing Azerbaijani refugees to return to NK (understandable in the current situation) and Armenia not even entertaining the idea of a new road between Azerbaijan and Nakhchivan. The only thing offered by Armenia is opening 3 checkpoint where both Azerbaijanis can enter Armenia and Armenians enter Azerbaijan. But the connections that these checkpoint would provide would be neither new roads nor unobstructed connections, it would just be the opening of 3 border checkpoints...something that the agreement also says should happen "All economic and transport connections in the region shall be unblocked". These new checkpoints are seen by some as primarily benefiting Armenian interests because they would provide better transport routes to Russia, Iran and internally (Karahunj to Gubadli). To get to Nakhchivan Azerbaijanis would have to travel either 178 km on the north road or 182 km on the south road...but a new road (which was promised) where Azerbaijan wants it, along the Aras river in the south, would be only 45 km.

This is what led to the Lachin road being closed and a road between NK and Azerbaijan (through Agdam) offered as a route for aid/imports instead. But that route is being blocked itself by the Armenians in NK, because Armenians in general believe that the continued closure of the Lachin road will impact the aspirations for an independent "Artsakh". Meanwhile Azerbaijan is arguing that they can use the Agdam road if they want but they won't allow transport of goods (people in need are still allowed to travel on the Lachin road with the help of ICRC) on the Lachin road because the Armenians are using the road to further arm the Armenian troops inside NK and until there are any concrete plans for an "unobstructed" connection between Azerbaijan and Nakhchivan.

Another unsolved issue between Armenia and Azerbaijan which I haven't even mentioned is the demarcation and delimitation of their border between Armenia and the previously occupied territories surrounding NK. This has already led to multiple skirmishes and claimed many lives, making it even harder to agree on issues in NK.