As a QuickBooks user and QB/IT support tech for 30 years I too experienced this issue where upon importing the cycle count Excel sheet I got a message “Cannot Import Cycle Count”. I am also a ProAdvisor. 

Turns out, for me, the issue was resolved by opening a new blank Excel spreadsheet on the same computer the file was exported to. Then I copied and pasted the data (with formatting) into the new spreadsheet; saved it then reimported and it worked!

Upon further investigation, I discovered that the user who was performing the cycle count moved the cycle count export spreadsheet to another computer with a different version of Excel. I suspect there are some subtle formatting and functionality elements in Excel that the QuickBooks cycle count export/import process requires to operate properly. By creating a new spreadsheet on the original Excel version used for the export, then copying in the data, with formatting, from the exported spreadsheet that had been saved in different version, I believe these required formatting and sheet functions were reinstated. This allowed the process to complete.

Of course, what is very frustrating is the alert messaging was completely erroneous and misleading. In my case, the issue had absolutely nothing to do with the server, internet access or the current login session. 

As a ProAdvisor agent recently advised we discussed the challenges for most users to migrate to QBO, "QuickBooks for desktop is being phased out". Issues like this, the enormous challenge to obtain higher level support on this issue and the responses from Intuit in this forum seem a clear indication that the agent’s advisement has merit.