VMware only presents a wired Ethernet connection to the Guest OS. This is normal and expected as the virtual network adapter defined in the virtual hardware is after all a wired network adapter not a Wi-Fi network adapter. BTW... On a related note, if at any time you're doing something that requires a Wi-Fi network adapter in the Guest OS then you'll need to provide your own USB Wi-Fi network adapter to connect directly to the VM.
As to the loss of network connectivity after closing VMware Player, sorry I haven't experienced that issue. To help diagnose/troubleshoot, you might provide some more technical details about your network environment and also how the VM's network adapter is configured, e.g NAT or Bridged. Also, is this an issue every time or is it intermittent?
