Limitations On The Sheet.Copy Method

I have a macro that copys a worksheet a user-inputted number of times but throws an error after adding Sheet #62. The line it hangs on is:

Sheets(myTemplate).Copy After:=Sheets(i - 1)

Does anyone know if this is a problem with my code, a memory issue, or the workbook I'm using to copy? In the past when I've copied a lot of sheets in a workbook (to the same workbook), Excel sometimes won't let me add anymore but if I copy all the sheets to a new workbook it will sometimes let me add more sheets. I figured it was a problem with how Excel counts sheets.

Sub CopySheets()
myTemplate = ActiveSheet.Name

'First, jump through the validation hoops
Dim AddSheetQuestion As Variant

'Define the application input box question
showAddSheetQuestion:
AddSheetQuestion = Application.InputBox("Please enter the number of sheets you want to add," & vbCrLf & _
"or click the Cancel button to cancel the addition:", _
"How many sheets do you want to add?")

'Cancel or the X was clicked
If AddSheetQuestion = False Then..................................