I just ran into this problem with a new image I had created, instead of cloning from my previous images.

For me, it was a case of forgetting to apply the Microsoft Hotfix for the VMXNET 3 adapter when using Windows 7.  All of my existing images already had this fix applied.

Your problem might be different, but here is what I found and how I fixed it.

When I took a closer look at the LAN adapters in the composed desktop, the LAN adapter name had a number at the end, indicating it was a new adapter and not a re-use of the base image's NIC.  For example, the adapter name was Local Area Connection #2 or #3 or the active network name was my domain #2 or my domain #3.

To resolve the issue:

1. I removed the NIC from the base image using Edit Settings in the vSphere Web Client
2. I mounted an .ISO I created that includes Microsoft Hotfix from VMware KB 2007319, which will refer you to either Microsoft KB 2344941 for Windows 7 or, as is my case, Microsoft KB 2550978 for Windows 7 with SP1
   This includes the following .msu installation files, depending on my version of Windows 7 with SP1, which I put onto my ISO
   Windows6.1-KB2550978-x64.msu
   Windows6.1-KB2550978-x86.msu
3. I installed the appropriate .msu file, either 64-bit or 32-bit and rebooted the base image from my ISO
4. Then I shutdown the base image VM, Edit the settings again,
   1. Dismount the CD by connecting it back to client device
   2. Add the VMXNET 3 adapter back and set it to the correct network
5. Boot up the base image, edit the network adapter properties to disable IPv6
6. Shutdown the base image again
7. Take a new snapshot
8. Recompose the pool using the updated snapshot

When I logged into the composed desktop, the network adapter no longer has a number appended to it and IPv6 is still disabled.

I learned about this Microsoft Hotfix from VMware KB article 2007319, which is not the same exact issue, but the Hotfix resolves the issue, at least for me it does.