Thanks to all who contributed to this thread. It helped us to solve this issue that was bugging us for months.
We solved the problem by TICKING "allow the computer to turn off the device to save power" on the power management tab of the LAN NIC.
If this is not ticked, the NIC stays powered on (ready for updates, maintenance, etc) during sleep.
If this is ticked, the NIC turns off in sleep state and gets re-initialized upon resume from sleep and network will be available immediately.
One drawback is that the computer does not respond to e.g. magic packets. However, most companies do not use magic packets for security and other reasons, thus most of us can live with it.
On a side note: If you change the power settings for laptops, bear in mind that you should not allow the NIC to awake the computer from sleep. If you do, it will definitely happen that laptops will be turned on randomly while they are in their bags because
the NIC has a funny moment, causing hardware damage because of overheating, battery deterioration and in worst case even loss of work.